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Discussiones Mathematicae - General Algebra and Applications最新文献

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Introduction to Third-Order Jacobsthal and Modified Third-Order Jacobsthal Hybrinomials 三阶jacobthal和修正三阶jacobthal杂交项简介
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1349
Gamaliel Cerda-Morales
{"title":"Introduction to Third-Order Jacobsthal and Modified Third-Order Jacobsthal Hybrinomials","authors":"Gamaliel Cerda-Morales","doi":"10.7151/dmgaa.1349","DOIUrl":"https://doi.org/10.7151/dmgaa.1349","url":null,"abstract":"Abstract The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper, we introduce and study the third-order Jacobsthal and modified third-order Jacobsthal hybrinomials, i.e., polynomials, which are a generalization of the Jacobsthal hybrid numbers and the Jacobsthal-Lucas hybrid numbers, respectively.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"139 - 152"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46214069","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}
引用次数: 0
On Isoclinic Extensions of Lie Algebras and Nilpotent Lie Algebras 李代数与幂零李代数的等斜扩展
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1346
H. Arabyani, Mohammad Javad Sadeghifard
{"title":"On Isoclinic Extensions of Lie Algebras and Nilpotent Lie Algebras","authors":"H. Arabyani, Mohammad Javad Sadeghifard","doi":"10.7151/dmgaa.1346","DOIUrl":"https://doi.org/10.7151/dmgaa.1346","url":null,"abstract":"Abstract In this paper, we present the concept of isoclinism of Lie algebras and its relationship to the Schur multiplier of Lie algebras. Moreover, we prove some properties of a pair of nilpotent Lie algebras.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"15 - 22"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46144102","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}
引用次数: 0
Join Irreducible 2-Testable Semigroups 连接不可约2-可测试半群
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1354
Edmond W. H. Lee
{"title":"Join Irreducible 2-Testable Semigroups","authors":"Edmond W. H. Lee","doi":"10.7151/dmgaa.1354","DOIUrl":"https://doi.org/10.7151/dmgaa.1354","url":null,"abstract":"Abstract A nontrivial pseudovariety is join irreducible if whenever it is contained in the complete join of some collection of pseudovarieties, then it is contained in one of the pseudovarieties. A finite semigroup is join irreducible if it generates a join irreducible pseudovariety. The present article is concerned with semigroups that are 2-testable in the sense that they satisfy any equation formed by a pair of words that begin with the same variable, end with the same variable, and share the same set of factors of length two. The main objective is to show that there exist precisely seven join irreducible pseudovarieties of 2-testable semigroups. As a consequence, it is decidable in quadratic time if a finite 2-testable semigroup is join irreducible.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"103 - 112"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45425367","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}
引用次数: 0
Some Analogues of Topological Groups 拓扑群的一些类似物
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1357
M. Ram
{"title":"Some Analogues of Topological Groups","authors":"M. Ram","doi":"10.7151/dmgaa.1357","DOIUrl":"https://doi.org/10.7151/dmgaa.1357","url":null,"abstract":"Abstract Let (G, ∗) be a group and τ be a topology on G. Let τα = {A ⊆G : A ⊆ Int(Cl(Int(A)))}, g ∗ τ = {g ∗ A : A ∈ τ} for g ∈ G. In this paper, we establish two relations between G and τ under which it follows that g ∗ τ ⊆ τα and g ∗ τα ⊆ τα, designate them by α-topological groups and α-irresolute topological groups, respectively. We indicate that under what conditions an α-topological group is topological group. This paper also covers some general properties and characterizations of α-topological groups and α-irresolute topological groups. In particular, we prove that (1) the product of two α-topological groups is α-topological group, (2) if H is a subgroup of an α-irresolute topological group, then αInt(H) is also subgroup, and (3) if A is an α-open subset of an α-irresolute topological group, then < A > is also α−open. In the mid of discourse, we also mention about their relationships with some existing spaces.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"171 - 181"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46671373","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}
引用次数: 1
Normalized Laplacian Spectrum of Some Q-Coronas of Two Regular Graphs 两个正则图的若干q -冕的归一化拉普拉斯谱
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1352
Arpita Das, P. Panigrahi
{"title":"Normalized Laplacian Spectrum of Some Q-Coronas of Two Regular Graphs","authors":"Arpita Das, P. Panigrahi","doi":"10.7151/dmgaa.1352","DOIUrl":"https://doi.org/10.7151/dmgaa.1352","url":null,"abstract":"Abstract In this paper we determine the normalized Laplacian spectrum of the Q-vertex corona, Q-edge corona, Q-vertex neighborhood corona, and Q-edge neighborhood corona of a connected regular graph with an arbitrary regular graph in terms of normalized Laplacian eigenvalues of the original graphs. Moreover, applying these results we find some non-regular normalized Laplacian co-spectral graphs.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"127 - 138"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44353899","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}
引用次数: 0
On Balancing Quaternions and Lucas-Balancing Quaternions 关于平衡四元数和Lucas平衡四元
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1348
D. Bród
{"title":"On Balancing Quaternions and Lucas-Balancing Quaternions","authors":"D. Bród","doi":"10.7151/dmgaa.1348","DOIUrl":"https://doi.org/10.7151/dmgaa.1348","url":null,"abstract":"Abstract In this paper we define and study balancing quaternions and Lucas-balancing quaternions. We give the generating functions, matrix generators and Binet formulas for these numbers. Moreover, the well-known properties e.g. Catalan, d’ Ocagne identities have been obtained for these quaternions.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"55 - 68"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47594129","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}
引用次数: 0
On the Skew Lie Product and Derivations of Prime Rings with Involution 关于有对合的素环的斜李积及其推导
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1355
M. R. Mozumder, N. Dar, Mohammad Salahuddin Khan, A. Abbasi̇
{"title":"On the Skew Lie Product and Derivations of Prime Rings with Involution","authors":"M. R. Mozumder, N. Dar, Mohammad Salahuddin Khan, A. Abbasi̇","doi":"10.7151/dmgaa.1355","DOIUrl":"https://doi.org/10.7151/dmgaa.1355","url":null,"abstract":"Abstract Let R be a ring with involution ′∗′. The skew Lie product of a, b ∈ R is defined by ∗[a, b] = ab − ba∗. The purpose of this paper is to study the commutativity of a prime ring which satisfies the various ∗-differential identities involving skew Lie product. Finally, we provide two examples to prove that the assumed restrictions on some of our results are not superfluous.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"183 - 194"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46923300","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}
引用次数: 0
On the Genus of the Idempotent Graph of a Finite Commutative Ring 关于有限交换环的幂等图的亏格
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1347
G. G. Belsi, S. Kavitha, K. Selvakumar
{"title":"On the Genus of the Idempotent Graph of a Finite Commutative Ring","authors":"G. G. Belsi, S. Kavitha, K. Selvakumar","doi":"10.7151/dmgaa.1347","DOIUrl":"https://doi.org/10.7151/dmgaa.1347","url":null,"abstract":"Abstract Let R be a finite commutative ring with identity. The idempotent graph of R is the simple undirected graph I(R) with vertex set, the set of all nontrivial idempotents of R and two distinct vertices x and y are adjacent if and only if xy = 0. In this paper, we have determined all isomorphism classes of finite commutative rings with identity whose I(R) has genus one or two. Also we have determined all isomorphism classes of finite commutative rings with identity whose I(R) has crosscap one. Also we study the the book embedding of toroidal idempotent graphs and classify finite commutative rings whose I(R) is a ring graph.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"23 - 31"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47587433","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}
引用次数: 1
Representation and Construction of Intuitionistic Fuzzy 𝒯 -Preorders and Fuzzy Weak 𝒯 -Orders 直觉模糊预序和模糊弱序的表示与构造
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1345
Brahim Ziane, A. Amroune
{"title":"Representation and Construction of Intuitionistic Fuzzy 𝒯 -Preorders and Fuzzy Weak 𝒯 -Orders","authors":"Brahim Ziane, A. Amroune","doi":"10.7151/dmgaa.1345","DOIUrl":"https://doi.org/10.7151/dmgaa.1345","url":null,"abstract":"Abstract In this paper, we consider the problem of representation and construction of intuitionistic fuzzy preorders and weak orders, where many fundamental representation results extending those of Ulrich Bodenhofer et al. are presented.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"81 - 101"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44572587","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}
引用次数: 0
Graded Hopf Algebras and the Descent Gebra 分级Hopf代数与下降代数
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-01-01 DOI: 10.1007/978-3-030-77845-3_5
P. Cartier, F. Patras
{"title":"Graded Hopf Algebras and the Descent Gebra","authors":"P. Cartier, F. Patras","doi":"10.1007/978-3-030-77845-3_5","DOIUrl":"https://doi.org/10.1007/978-3-030-77845-3_5","url":null,"abstract":"","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91218910","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}
引用次数: 0
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