Pub Date : 2023-08-18DOI: 10.1142/s0218196723500625
M. Campercholi, D. Vaggione
{"title":"A short proof of the Baker-Pixley theorem for classes","authors":"M. Campercholi, D. Vaggione","doi":"10.1142/s0218196723500625","DOIUrl":"https://doi.org/10.1142/s0218196723500625","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47297716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-18DOI: 10.1142/s0218196723500613
V. Bardakov, O. V. Bryukhanov, M. V. Neshchadim
{"title":"On Residual Nilpotence of Group Extensions","authors":"V. Bardakov, O. V. Bryukhanov, M. V. Neshchadim","doi":"10.1142/s0218196723500613","DOIUrl":"https://doi.org/10.1142/s0218196723500613","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46055691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-23DOI: 10.1142/s0218196723500510
A. Tuganbaev
{"title":"ℵ0-Distributive Modules and Rings","authors":"A. Tuganbaev","doi":"10.1142/s0218196723500510","DOIUrl":"https://doi.org/10.1142/s0218196723500510","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42314591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-16DOI: 10.1142/s0218196723500509
L. Miller, William D. Taylor, J. Vassilev
{"title":"Differentially Fixed Ideals in Affine Semigroup Rings","authors":"L. Miller, William D. Taylor, J. Vassilev","doi":"10.1142/s0218196723500509","DOIUrl":"https://doi.org/10.1142/s0218196723500509","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46983318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.1142/s0218196723500364
Boris Kunyavski, Vadim Z. Ostapenko
The Tate–Shafarevich set of a group [Formula: see text] defined by Takashi Ono coincides, in the case where [Formula: see text] is finite, with the group of outer class-preserving automorphisms of [Formula: see text] introduced by Burnside. We consider analogs of this important group-theoretic object for Lie algebras and associative algebras and establish some new structure properties thereof. We also discuss open problems and eventual generalizations to other algebraic structures.
{"title":"Tate–Shafarevich groups and algebras","authors":"Boris Kunyavski, Vadim Z. Ostapenko","doi":"10.1142/s0218196723500364","DOIUrl":"https://doi.org/10.1142/s0218196723500364","url":null,"abstract":"The Tate–Shafarevich set of a group [Formula: see text] defined by Takashi Ono coincides, in the case where [Formula: see text] is finite, with the group of outer class-preserving automorphisms of [Formula: see text] introduced by Burnside. We consider analogs of this important group-theoretic object for Lie algebras and associative algebras and establish some new structure properties thereof. We also discuss open problems and eventual generalizations to other algebraic structures.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135626590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-21DOI: 10.1142/s0218196723500285
Moses Ganardi, Markus Lohrey, Georg Zetzsche
We prove that the power word problem for certain metabelian subgroups of [Formula: see text] (including the solvable Baumslag–Solitar groups [Formula: see text]) belongs to the circuit complexity class [Formula: see text]. In the power word problem, the input consists of group elements [Formula: see text] and binary encoded integers [Formula: see text] and it is asked whether [Formula: see text] holds. Moreover, we prove that the knapsack problem for [Formula: see text] is [Formula: see text]-complete. In the knapsack problem, the input consists of group elements [Formula: see text] and it is asked whether the equation [Formula: see text] has a solution in [Formula: see text]. For the more general case of a system of so-called exponent equations, where the exponent variables [Formula: see text] can occur multiple times, we show that solvability is undecidable for [Formula: see text].
证明了[公式:见文]的某些亚元子群(包括可解的Baumslag-Solitar群[公式:见文])的幂词问题属于电路复杂度类[公式:见文]。在幂词问题中，输入由群元素[Formula: see text]和二进制编码的整数[Formula: see text]组成，并询问[Formula: see text]是否成立。此外，我们证明了[公式:见文]的背包问题是[公式:见文]完全的。在背包问题中，输入由群元素[公式:见文]组成，问方程[公式:见文]在[公式:见文]中是否有解。对于所谓的指数方程系统的更一般的情况，其中指数变量[公式:见文本]可以出现多次，我们表明可解性是不可判定的[公式:见文本]。
{"title":"Knapsack and the power word problem in solvable Baumslag–Solitar groups","authors":"Moses Ganardi, Markus Lohrey, Georg Zetzsche","doi":"10.1142/s0218196723500285","DOIUrl":"https://doi.org/10.1142/s0218196723500285","url":null,"abstract":"We prove that the power word problem for certain metabelian subgroups of [Formula: see text] (including the solvable Baumslag–Solitar groups [Formula: see text]) belongs to the circuit complexity class [Formula: see text]. In the power word problem, the input consists of group elements [Formula: see text] and binary encoded integers [Formula: see text] and it is asked whether [Formula: see text] holds. Moreover, we prove that the knapsack problem for [Formula: see text] is [Formula: see text]-complete. In the knapsack problem, the input consists of group elements [Formula: see text] and it is asked whether the equation [Formula: see text] has a solution in [Formula: see text]. For the more general case of a system of so-called exponent equations, where the exponent variables [Formula: see text] can occur multiple times, we show that solvability is undecidable for [Formula: see text].","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"181 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135416152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-22DOI: 10.1142/S0218196723500601
P. Aglianó, S. Bartali, S. Fioravanti
In this paper we explore some applications of a certain technique (that we call the Freese's technique), which is a tool for identifying certain lattices as sublattices of the congruence lattice of a given algebra. In particular we will give sufficient conditions for two family of lattices (called the rods and the snakes) to be admissible as sublattices of a variety generated by a given algebra, extending an unpublished result of R. Freese and P. Lipparini.
{"title":"On freese's technique","authors":"P. Aglianó, S. Bartali, S. Fioravanti","doi":"10.1142/S0218196723500601","DOIUrl":"https://doi.org/10.1142/S0218196723500601","url":null,"abstract":"In this paper we explore some applications of a certain technique (that we call the Freese's technique), which is a tool for identifying certain lattices as sublattices of the congruence lattice of a given algebra. In particular we will give sufficient conditions for two family of lattices (called the rods and the snakes) to be admissible as sublattices of a variety generated by a given algebra, extending an unpublished result of R. Freese and P. Lipparini.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47491239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-14DOI: 10.1142/s0218196723500558
Richard Mandel, A. Ushakov
For a finitely generated group $G$, the emph{Diophantine problem} over $G$ is the algorithmic problem of deciding whether a given equation $W(z_1,z_2,ldots,z_k) = 1$ (perhaps restricted to a fixed subclass of equations) has a solution in $G$. In this paper, we investigate the algorithmic complexity of the Diophantine problem for the class $mathcal{C}$ of quadratic equations over the metabelian Baumslag-Solitar groups $mathbf{BS}(1,n)$. We prove that this problem is $mathbf{NP}$-complete whenever $nneq pm 1$, and determine the algorithmic complexity for various subclasses (orientable, nonorientable etc.) of $mathcal{C}$.
{"title":"Quadratic equations in metabelian Baumslag-Solitar groups","authors":"Richard Mandel, A. Ushakov","doi":"10.1142/s0218196723500558","DOIUrl":"https://doi.org/10.1142/s0218196723500558","url":null,"abstract":"For a finitely generated group $G$, the emph{Diophantine problem} over $G$ is the algorithmic problem of deciding whether a given equation $W(z_1,z_2,ldots,z_k) = 1$ (perhaps restricted to a fixed subclass of equations) has a solution in $G$. In this paper, we investigate the algorithmic complexity of the Diophantine problem for the class $mathcal{C}$ of quadratic equations over the metabelian Baumslag-Solitar groups $mathbf{BS}(1,n)$. We prove that this problem is $mathbf{NP}$-complete whenever $nneq pm 1$, and determine the algorithmic complexity for various subclasses (orientable, nonorientable etc.) of $mathcal{C}$.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43872859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Jaya Subba Reddy, M. Sri Kameswara Rao, O. Vishal, Preethi Budi
Let 𝑅 be a prime ring
设𝑅为素环
{"title":"Generalized (σ,τ)-reverse derivations in prime rings","authors":"C. Jaya Subba Reddy, M. Sri Kameswara Rao, O. Vishal, Preethi Budi","doi":"10.12988/ija.2023.91739","DOIUrl":"https://doi.org/10.12988/ija.2023.91739","url":null,"abstract":"Let 𝑅 be a prime ring","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"35 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80796596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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