Pub Date : 2022-02-24DOI: 10.1142/s0218196722500230
Chris Köcher
Partially lossy queue monoids (plq monoids) model the behavior of queues that can non-deterministically forget specified parts of their content at any time. We call the subsets of this monoid partially lossy queue languages (plq languages). While many decision problems on recognizable plq languages are decidable, most of them are undecidable if the languages are rational. In particular, in this monoid the classes of rational and recognizable languages do not coincide. This is due to the fact that the class of recognizable plq languages is not closed under multiplication and iteration. However, we can generate the recognizable plq languages using special rational expressions consisting of the Boolean operations and restricted versions of multiplication and iteration. From these special rational expressions we can also obtain an MSO logic describing the recognizable plq languages. Moreover, we provide similar results for the class of aperiodic languages in the plq monoid.
{"title":"Rational, recognizable, and aperiodic partially lossy queue languages","authors":"Chris Köcher","doi":"10.1142/s0218196722500230","DOIUrl":"https://doi.org/10.1142/s0218196722500230","url":null,"abstract":"Partially lossy queue monoids (plq monoids) model the behavior of queues that can non-deterministically forget specified parts of their content at any time. We call the subsets of this monoid partially lossy queue languages (plq languages). While many decision problems on recognizable plq languages are decidable, most of them are undecidable if the languages are rational. In particular, in this monoid the classes of rational and recognizable languages do not coincide. This is due to the fact that the class of recognizable plq languages is not closed under multiplication and iteration. However, we can generate the recognizable plq languages using special rational expressions consisting of the Boolean operations and restricted versions of multiplication and iteration. From these special rational expressions we can also obtain an MSO logic describing the recognizable plq languages. Moreover, we provide similar results for the class of aperiodic languages in the plq monoid.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80411638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-24DOI: 10.1142/s0218196722500308
A. Drápal, T. Griggs, Andrew R. Kozlik
Let the product of points [Formula: see text] and [Formula: see text] be the vertex [Formula: see text] of the right isosceles triangle for which [Formula: see text] is the base, and [Formula: see text] is oriented anticlockwise. This yields a quasigroup that satisfies laws [Formula: see text], [Formula: see text] and [Formula: see text]. Such quasigroups are called quadratical. Quasigroups that satisfy only the latter two laws are equivalent to perfect Mendelsohn designs of length four ([Formula: see text]). This paper examines various algebraic identities induced by [Formula: see text], classifies finite quadratical quasigroups, and shows how the square structure of quadratical quasigroups is associated with toroidal grids.
{"title":"Quadratical quasigroups and Mendelsohn designs","authors":"A. Drápal, T. Griggs, Andrew R. Kozlik","doi":"10.1142/s0218196722500308","DOIUrl":"https://doi.org/10.1142/s0218196722500308","url":null,"abstract":"Let the product of points [Formula: see text] and [Formula: see text] be the vertex [Formula: see text] of the right isosceles triangle for which [Formula: see text] is the base, and [Formula: see text] is oriented anticlockwise. This yields a quasigroup that satisfies laws [Formula: see text], [Formula: see text] and [Formula: see text]. Such quasigroups are called quadratical. Quasigroups that satisfy only the latter two laws are equivalent to perfect Mendelsohn designs of length four ([Formula: see text]). This paper examines various algebraic identities induced by [Formula: see text], classifies finite quadratical quasigroups, and shows how the square structure of quadratical quasigroups is associated with toroidal grids.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83509066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-21DOI: 10.1142/s0218196723500200
K. Kearnes
We show that, when restricted to the class of varieties that have a Taylor term, several commutator properties are definable by Maltsev conditions.
我们证明，当限制到一类具有泰勒项的变元时，若干对易子性质可由Maltsev条件定义。
{"title":"Relative Maltsev definability of some commutator properties","authors":"K. Kearnes","doi":"10.1142/s0218196723500200","DOIUrl":"https://doi.org/10.1142/s0218196723500200","url":null,"abstract":"We show that, when restricted to the class of varieties that have a Taylor term, several commutator properties are definable by Maltsev conditions.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82287459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-21DOI: 10.1142/s0218196722500333
A. Dzhumadil'daev, N. Ismailov, B. Sartayev
We prove that the class of algebras embeddable into Leibniz algebras with respect to the commutator product is not a variety. It is shown that every commutative metabelain algebra is embeddable into Leibniz algebras with respect to the anti-commutator. Furthermore, we study polynomial identities satisfied by the commutator in every Leibniz algebra. We extend the result of Dzhumadil’daev in [A. S. Dzhumadil’daev, [Formula: see text]-Leibniz algebras, Serdica Math. J. 34(2) (2008) 415–440]. to identities up to degree 7 and give a conjecture on identities of higher degrees. As a consequence, we obtain an example of a non-Spechtian variety of anticommutative algebras.
{"title":"On the commutator in Leibniz algebras","authors":"A. Dzhumadil'daev, N. Ismailov, B. Sartayev","doi":"10.1142/s0218196722500333","DOIUrl":"https://doi.org/10.1142/s0218196722500333","url":null,"abstract":"We prove that the class of algebras embeddable into Leibniz algebras with respect to the commutator product is not a variety. It is shown that every commutative metabelain algebra is embeddable into Leibniz algebras with respect to the anti-commutator. Furthermore, we study polynomial identities satisfied by the commutator in every Leibniz algebra. We extend the result of Dzhumadil’daev in [A. S. Dzhumadil’daev, [Formula: see text]-Leibniz algebras, Serdica Math. J. 34(2) (2008) 415–440]. to identities up to degree 7 and give a conjecture on identities of higher degrees. As a consequence, we obtain an example of a non-Spechtian variety of anticommutative algebras.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79888713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-17DOI: 10.1142/s0218196722500278
Zhi-wei Li, Xiaojin Zhang
We study (support) [Formula: see text]-tilting modules over the trivial extensions of finite-dimensional algebras. More precisely, we construct two classes of (support)[Formula: see text]-tilting modules in terms of the adjoint functors which extend and generalize the results on (support) [Formula: see text]-tilting modules over triangular matrix rings given by Gao-Huang.
{"title":"Τ-tilting Modules over Trivial Extensions","authors":"Zhi-wei Li, Xiaojin Zhang","doi":"10.1142/s0218196722500278","DOIUrl":"https://doi.org/10.1142/s0218196722500278","url":null,"abstract":"We study (support) [Formula: see text]-tilting modules over the trivial extensions of finite-dimensional algebras. More precisely, we construct two classes of (support)[Formula: see text]-tilting modules in terms of the adjoint functors which extend and generalize the results on (support) [Formula: see text]-tilting modules over triangular matrix rings given by Gao-Huang.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74972118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-17DOI: 10.1142/s0218196722500163
M. Dixon, L. A. Kurdachenko, I. Subbotin
We introduce the concept of a conormal subgroup: a subgroup is conormal if it is contranormal in its normal closure. This unifies the concepts of normal and contranormal subgroups. We obtain some important properties of conormal subgroups, describe their connections with transitivity of normality, and study groups in which all conormal subgroups are normal.
{"title":"On conormal subgroups","authors":"M. Dixon, L. A. Kurdachenko, I. Subbotin","doi":"10.1142/s0218196722500163","DOIUrl":"https://doi.org/10.1142/s0218196722500163","url":null,"abstract":"We introduce the concept of a conormal subgroup: a subgroup is conormal if it is contranormal in its normal closure. This unifies the concepts of normal and contranormal subgroups. We obtain some important properties of conormal subgroups, describe their connections with transitivity of normality, and study groups in which all conormal subgroups are normal.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74906518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-11DOI: 10.1142/s0218196722500229
Jan Kim, Donghi Lee
In this paper, we construct a family of two types of finitely generated non-Hopfian groups with explicit presentations, where the first type satisfies small cancellation conditions [Formula: see text] and [Formula: see text], and interpret these groups as direct limits of relatively hyperbolic groups and ordinary hyperbolic groups, respectively.
{"title":"Construction of non-Hopfian groups as direct limits of relatively hyperbolic groups","authors":"Jan Kim, Donghi Lee","doi":"10.1142/s0218196722500229","DOIUrl":"https://doi.org/10.1142/s0218196722500229","url":null,"abstract":"In this paper, we construct a family of two types of finitely generated non-Hopfian groups with explicit presentations, where the first type satisfies small cancellation conditions [Formula: see text] and [Formula: see text], and interpret these groups as direct limits of relatively hyperbolic groups and ordinary hyperbolic groups, respectively.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81330397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-07DOI: 10.1142/s0218196722500114
N. Kim, Yang Lee, M. Ziembowski
In this paper, we study the annihilating properties of ideals generated by coefficients of polynomials and power series which satisfy a structural equation. We first show that if [Formula: see text] for polynomials [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] and [Formula: see text], whenever [Formula: see text] and [Formula: see text]. Next we prove that if [Formula: see text] for power series [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] when [Formula: see text] and [Formula: see text], [Formula: see text] for each [Formula: see text].
{"title":"Annihilating properties of ideals generated by coefficients of polynomials and power series","authors":"N. Kim, Yang Lee, M. Ziembowski","doi":"10.1142/s0218196722500114","DOIUrl":"https://doi.org/10.1142/s0218196722500114","url":null,"abstract":"In this paper, we study the annihilating properties of ideals generated by coefficients of polynomials and power series which satisfy a structural equation. We first show that if [Formula: see text] for polynomials [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] and [Formula: see text], whenever [Formula: see text] and [Formula: see text]. Next we prove that if [Formula: see text] for power series [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] when [Formula: see text] and [Formula: see text], [Formula: see text] for each [Formula: see text].","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76333521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-04DOI: 10.1142/s0218196723500467
Jiangtao Shi, Na Li, R. Shen
Let $G$ be a finite group and $p$ a fixed prime divisor of $|G|$. Combining the nilpotence, the normality and the order of groups together, we prove that if every maximal subgroup of $G$ is nilpotent or normal or has $p'$-order, then (1) $G$ is solvable; (2) $G$ has a Sylow tower; (3) There exists at most one prime divisor $q$ of $|G|$ such that $G$ is neither $q$-nilpotent nor $q$-closed, where $qneq p$.
{"title":"Finite groups in which every maximal subgroup is nilpotent or normal or has p′-order","authors":"Jiangtao Shi, Na Li, R. Shen","doi":"10.1142/s0218196723500467","DOIUrl":"https://doi.org/10.1142/s0218196723500467","url":null,"abstract":"Let $G$ be a finite group and $p$ a fixed prime divisor of $|G|$. Combining the nilpotence, the normality and the order of groups together, we prove that if every maximal subgroup of $G$ is nilpotent or normal or has $p'$-order, then (1) $G$ is solvable; (2) $G$ has a Sylow tower; (3) There exists at most one prime divisor $q$ of $|G|$ such that $G$ is neither $q$-nilpotent nor $q$-closed, where $qneq p$.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85040513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-31DOI: 10.1142/s021819672250014x
Takamichi Sato
We study subgroups of the group [Formula: see text] of piecewise linear orientation-preserving homeomorphisms of the unit interval [Formula: see text] that are differentiable everywhere except at finitely many real numbers, under the operation of composition. We provide a criterion for any two subgroups of [Formula: see text] which are direct products of finitely many indecomposable non-commutative groups to be non-isomorphic. As its application, we give a necessary and sufficient condition for any two subgroups of the R. Thompson group [Formula: see text] that are stabilizers of finite sets of numbers in the interval [Formula: see text] to be isomorphic, thus solving a problem by G. Golan and M. Sapir. We also show that if two stabilizers are isomorphic, then they are conjugate inside a certain group [Formula: see text].
{"title":"Direct decompositions of groups of piecewise linear homeomorphisms of the unit interval","authors":"Takamichi Sato","doi":"10.1142/s021819672250014x","DOIUrl":"https://doi.org/10.1142/s021819672250014x","url":null,"abstract":"We study subgroups of the group [Formula: see text] of piecewise linear orientation-preserving homeomorphisms of the unit interval [Formula: see text] that are differentiable everywhere except at finitely many real numbers, under the operation of composition. We provide a criterion for any two subgroups of [Formula: see text] which are direct products of finitely many indecomposable non-commutative groups to be non-isomorphic. As its application, we give a necessary and sufficient condition for any two subgroups of the R. Thompson group [Formula: see text] that are stabilizers of finite sets of numbers in the interval [Formula: see text] to be isomorphic, thus solving a problem by G. Golan and M. Sapir. We also show that if two stabilizers are isomorphic, then they are conjugate inside a certain group [Formula: see text].","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87498753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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