A new-type algebraic digital signature schemes on non-commutative associative algebras are developed using technique of performing exponentiation operations in a hidden group. The signature contains two elements: a randomization integer e and a vector S. The used verification equations are characterized in multiple entries of the signature element S. The post-quantum security of the introduced signature algorithms is provided by the computational difficulty of solving a system of many quadratic equations in many variables, like in the public-key multivariate cryptosystems. However in the former case the quadratic equations are set over the finite fields having the order of significantly larger size.
{"title":"Algebraic signature algorithms with a hidden group group, based on hardness of solving systems of quadratic equations","authors":"N. Moldovyan","doi":"10.56415/qrs.v30.24","DOIUrl":"https://doi.org/10.56415/qrs.v30.24","url":null,"abstract":"A new-type algebraic digital signature schemes on non-commutative associative algebras are developed using technique of performing exponentiation operations in a hidden group. The signature contains two elements: a randomization integer e and a vector S. The used verification equations are characterized in multiple entries of the signature element S. The post-quantum security of the introduced signature algorithms is provided by the computational difficulty of solving a system of many quadratic equations in many variables, like in the public-key multivariate cryptosystems. However in the former case the quadratic equations are set over the finite fields having the order of significantly larger size.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43746875","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}
The necessary and sufficient conditions under which a Menger algebra can be isomorphically represented by medial n-ary operations are proposed. Since a Menger hypercompositional algebra can be regarded as a generalization of a Menger algebra, for this reason, the situation for medial hyperoperations is further examined and a representation theorem of Menger hypercompositional algebras by such concepts is proved.
{"title":"Menger hypercompositional algebras represented by medial n-ary hyperoperations","authors":"T. Kumduang","doi":"10.56415/qrs.v30.22","DOIUrl":"https://doi.org/10.56415/qrs.v30.22","url":null,"abstract":"The necessary and sufficient conditions under which a Menger algebra can be isomorphically represented by medial n-ary operations are proposed. Since a Menger hypercompositional algebra can be regarded as a generalization of a Menger algebra, for this reason, the situation for medial hyperoperations is further examined and a representation theorem of Menger hypercompositional algebras by such concepts is proved.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43921335","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}
We introduce and study the concepts of 2-prime and n-weakly 2-prime (resp. weakly 2-prime) ideals in a commutative semiring. We prove that an integral semidomain S is a valuation semiring if and only if every proper ideal of S is 2-prime and in a principal ideal semidomain the concepts of primary, quasi-primary and 2-prime ideals coincide. We characterize semirings where 2-prime ideals are prime and also characterize semirings where every proper ideal is n-weakly 2-prime (resp. weakly 2-prime)
{"title":"A note on 2-prime and n-weakly 2-prime ideals of semirings","authors":"Biswaranjan Khanra, M. Mandal, S. Das","doi":"10.56415/qrs.v30.20","DOIUrl":"https://doi.org/10.56415/qrs.v30.20","url":null,"abstract":"We introduce and study the concepts of 2-prime and n-weakly 2-prime (resp. weakly 2-prime) ideals in a commutative semiring. We prove that an integral semidomain S is a valuation semiring if and only if every proper ideal of S is 2-prime and in a principal ideal semidomain the concepts of primary, quasi-primary and 2-prime ideals coincide. We characterize semirings where 2-prime ideals are prime and also characterize semirings where every proper ideal is n-weakly 2-prime (resp. weakly 2-prime)","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43909310","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}
The concept of quasi-ordered residuated systems was introduced by Bonzio and Chajda in 2018. The author introduced the concept of filters in such systems as well as some types of filters in them such as implicative and comparative filters. This article introduces the concept of a normal filter in a quasi-ordered residuated system and relates it to some other filters in such algebraic systems.
{"title":"Normal filter in quasi-ordered residuated system","authors":"D. Romano","doi":"10.56415/qrs.v30.27","DOIUrl":"https://doi.org/10.56415/qrs.v30.27","url":null,"abstract":"The concept of quasi-ordered residuated systems was introduced by Bonzio and Chajda in 2018. The author introduced the concept of filters in such systems as well as some types of filters in them such as implicative and comparative filters. This article introduces the concept of a normal filter in a quasi-ordered residuated system and relates it to some other filters in such algebraic systems.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45312911","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}
For a finite group G, let W(G) denotes the set of the orders of the elements of G. In this paper we study jW(G)j and show that the cyclic group of order n has the maximum value of jW(G)j among all groups of the same order. Furthermore we study this notion in nilpotent and non-nilpotent groups and state some inequality for it. Among the result we show that the minimum value of jW(G)j is power of 2 or it pertains to a non-nilpotent group.
{"title":"On the weight of finite groups","authors":"Mohammad Amin Morshedlo, M. M. Nasrabadi","doi":"10.56415/qrs.v30.25","DOIUrl":"https://doi.org/10.56415/qrs.v30.25","url":null,"abstract":"For a finite group G, let W(G) denotes the set of the orders of the elements of G. In this paper we study jW(G)j and show that the cyclic group of order n has the maximum value of jW(G)j among all groups of the same order. Furthermore we study this notion in nilpotent and non-nilpotent groups and state some inequality for it. Among the result we show that the minimum value of jW(G)j is power of 2 or it pertains to a non-nilpotent group.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42045071","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}
The aim of this paper is to review thoroughly the applications of ∩ -large pseudo N-injective acts in quasi-Frobenius monoid theory, and therefore, the relationship of ∩ -large pseudo N-injective acts with some class of injectivity is studied. Applications of the properties of ∩ -large pseudo injective acts in quasi-Frobenius monoid theory are proven. Also, it’s proved that the subsequent parity, every union (direct sum) of the two ∩ -large pseudo injective acts is a ∩ -large pseudo injective act if and only if every ∩ -large pseudo injective act is injective under Noetherian condition for a right monoid S. Additionally, we proved that the category of strongly ∩ -large pseudo N-injective right S-acts are going to be egalitarian to the category of projective right S-acts under monoid conditions. The connections between quasi injective and ∩ -large pseudo injective acts are investigated.
{"title":"Applications of $bigcap$-large pseudo N-injective acts in quasi-Frobenius monoid theory and its relationship with some classes of injectivity","authors":"S. Abdul-Kareem, A. A. Abdulkareem","doi":"10.56415/qrs.v30.16","DOIUrl":"https://doi.org/10.56415/qrs.v30.16","url":null,"abstract":"The aim of this paper is to review thoroughly the applications of ∩ -large pseudo N-injective acts in quasi-Frobenius monoid theory, and therefore, the relationship of ∩ -large pseudo N-injective acts with some class of injectivity is studied. Applications of the properties of ∩ -large pseudo injective acts in quasi-Frobenius monoid theory are proven. Also, it’s proved that the subsequent parity, every union (direct sum) of the two ∩ -large pseudo injective acts is a ∩ -large pseudo injective act if and only if every ∩ -large pseudo injective act is injective under Noetherian condition for a right monoid S. Additionally, we proved that the category of strongly ∩ -large pseudo N-injective right S-acts are going to be egalitarian to the category of projective right S-acts under monoid conditions. The connections between quasi injective and ∩ -large pseudo injective acts are investigated.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49484058","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}
We determine the structure of translatable isotopes of translatable quasigroups. Necessary and sufficient conditions are found for a bijection between two such isotopes to be an isomorphism. It is also proved that in a left cancellative, k-translatable magma, the value of k is unique.
{"title":"Translatable isotopes of translatable quasigroups","authors":"W. Dudek, R. Monzo","doi":"10.56415/qrs.v30.17","DOIUrl":"https://doi.org/10.56415/qrs.v30.17","url":null,"abstract":"We determine the structure of translatable isotopes of translatable quasigroups. Necessary and sufficient conditions are found for a bijection between two such isotopes to be an isomorphism. It is also proved that in a left cancellative, k-translatable magma, the value of k is unique.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45977918","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}
We investigate the results of a partially ordered ternary semigroup containing right bases and characterize when a non-empty subset of a partially ordered ternary semigroup is a right base. Moreover, we give a characterization of a right base of a partially ordered ternary semigroup to be a ternary subsemigroup and we show that the right bases of a partially ordered ternary semigroup have same cardinality. Finally, we show that the complement of the union of all right bases of a partially ordered ternary semigroup is a maximal proper left ideal.
{"title":"On right bases of partially ordered ternary semigroups","authors":"Wichayaporn Jantanan, Natee Raikham, R. Chinram","doi":"10.56415/qrs.v30.18","DOIUrl":"https://doi.org/10.56415/qrs.v30.18","url":null,"abstract":"We investigate the results of a partially ordered ternary semigroup containing right bases and characterize when a non-empty subset of a partially ordered ternary semigroup is a right base. Moreover, we give a characterization of a right base of a partially ordered ternary semigroup to be a ternary subsemigroup and we show that the right bases of a partially ordered ternary semigroup have same cardinality. Finally, we show that the complement of the union of all right bases of a partially ordered ternary semigroup is a maximal proper left ideal.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46115738","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}
We introduce the notion of a left-twisted ring, and we construct a left-zero ring which is not a ring. We show that such a left-twisted ring does not have an identity. Also, we show that every non-zero element of the left-twisted ring is a pseudo unit of it.
{"title":"Left twisted rings","authors":"H. Kim, Jae Hee Kim","doi":"10.56415/qrs.v30.21","DOIUrl":"https://doi.org/10.56415/qrs.v30.21","url":null,"abstract":"We introduce the notion of a left-twisted ring, and we construct a left-zero ring which is not a ring. We show that such a left-twisted ring does not have an identity. Also, we show that every non-zero element of the left-twisted ring is a pseudo unit of it.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41278757","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}
In this paper, we establish the necessary and sufficient condition for an equivalence relation ρ on an S-act A endowed with a topology such that A/ρ becomes a Hausdorff topological S-act. Also, we show that if A1 and A2 be two topological S-acts, then for any homomorphism ϕ : A1 → A2, A1/ ker ϕ is a topological S-act if and only if ϕ is ϕ-saturated continuous. Moreover, we establish for any two congruences θ1 and θ2 on an S-act A endowed with a topology, θ1 ∩ θ2 is a topological S-act congruence on A if and only if the mapping ϕ : A → A/θ1 × A/θ2, defined by ϕ(a) = (aθ1, aθ2), for all a ∈ A, is ϕ-saturated continuous, where S is a topological semigroup.
本文建立了具有拓扑的s -行为A上等价关系ρ使A/ρ成为Hausdorff拓扑s -行为的充分必要条件。同样，我们证明了如果A1和A2是两个拓扑s行为，那么对于任意同态φ: A1→A2, A1/ ker φ是一个拓扑s行为当且仅当φ是ϕ-饱和连续的。此外，我们建立了对于给定拓扑的S-行为A上的任意两个同余θ1和θ2， θ1∩θ2是A上的拓扑S-行为同余当且仅当映射φ: A→A/θ1 × A/θ2，定义为φ (A) = (A θ1, A θ2)，对于所有A∈A，是ϕ-饱和连续的，其中S是拓扑半群。
{"title":"Topological S-act congruence","authors":"S. Maity, Monika Paul","doi":"10.56415/qrs.v30.23","DOIUrl":"https://doi.org/10.56415/qrs.v30.23","url":null,"abstract":"In this paper, we establish the necessary and sufficient condition for an equivalence relation ρ on an S-act A endowed with a topology such that A/ρ becomes a Hausdorff topological S-act. Also, we show that if A1 and A2 be two topological S-acts, then for any homomorphism ϕ : A1 → A2, A1/ ker ϕ is a topological S-act if and only if ϕ is ϕ-saturated continuous. Moreover, we establish for any two congruences θ1 and θ2 on an S-act A endowed with a topology, θ1 ∩ θ2 is a topological S-act congruence on A if and only if the mapping ϕ : A → A/θ1 × A/θ2, defined by ϕ(a) = (aθ1, aθ2), for all a ∈ A, is ϕ-saturated continuous, where S is a topological semigroup.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44642948","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：