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International Journal of Algebra and Computation最新文献

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An investigation of numerical semigroups of embedding dimension 4 through GAP 利用GAP研究嵌入维数为4的数值半群
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2023-01-01 DOI: 10.12988/ija.2023.91732
Merita Bajrami, D. Dimovski, Violeta Angjelkoska
{"title":"An investigation of numerical semigroups of embedding dimension 4 through GAP","authors":"Merita Bajrami, D. Dimovski, Violeta Angjelkoska","doi":"10.12988/ija.2023.91732","DOIUrl":"https://doi.org/10.12988/ija.2023.91732","url":null,"abstract":"We reformulate the examinations of the Apéry set of a numerical semigroup of embedding dimension 4 with respect to a generator n to the examinations of a presentation of the cyclic group of order n , by three generators and three relations. We examine such presentations using the GAP package","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79715930","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}
引用次数: 0
Four dimensional absolute valued algebras having two different subalgebras isomorphic to C 具有与C同构的两个不同子代数的四维绝对值代数
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2023-01-01 DOI: 10.12988/ija.2023.91737
A. Moutassim, Mohamed Louzari, Aziz Es. Sadiq
{"title":"Four dimensional absolute valued algebras having two different subalgebras isomorphic to C","authors":"A. Moutassim, Mohamed Louzari, Aziz Es. Sadiq","doi":"10.12988/ija.2023.91737","DOIUrl":"https://doi.org/10.12988/ija.2023.91737","url":null,"abstract":"The aim of this paper is to construct, by algebraic methods, some new class of four-dimensional absolute valued algebras, namely M 1 , M 2 and M 3 which are not isomorphic to the known algebra H . These new algebras contain a nonzero omnipresent idempotent. Furthermore, we classify all four-dimensional absolute valued algebras having two dif-ferent subalgebras isomorphic to C . Note that there exists a four-dimensional absolute valued algebra containing no subalgebra of dimension two, which means that, the problem of classifying all four-dimensional absolute valued algebras seems still to be open.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79800618","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}
引用次数: 1
Some commutativity theorems in rings with involution involving generalized reverse derivations 涉及广义逆导对合环的交换性定理
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2023-01-01 DOI: 10.12988/ija.2023.91773
C. Jaya, Subba Reddy, V.S.V. Krishna Murty, Preethi Budi, D. Dheeraj
{"title":"Some commutativity theorems in rings with involution involving generalized reverse derivations","authors":"C. Jaya, Subba Reddy, V.S.V. Krishna Murty, Preethi Budi, D. Dheeraj","doi":"10.12988/ija.2023.91773","DOIUrl":"https://doi.org/10.12988/ija.2023.91773","url":null,"abstract":"In this paper we prove some results about the commutativity of the rings with involution of second kind satisfying certain conditions involving generalized reverse derivations. We also extend these results for generalized reverse derivations of prime rings to ideals. The aim of the present paper is to establish some results on commutativity of generalized reverse ∗ -derivations","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"20 7 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83919417","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}
引用次数: 0
On graded torsion free and graded injective k[x] modules 关于梯度无扭和梯度内射k[x]模
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2023-01-01 DOI: 10.12988/ija.2023.91735
William Todd Ashby
{"title":"On graded torsion free and graded injective k[x] modules","authors":"William Todd Ashby","doi":"10.12988/ija.2023.91735","DOIUrl":"https://doi.org/10.12988/ija.2023.91735","url":null,"abstract":"Much information about rings can be gained by studying their modules, and similarly, graded rings can be studied by studying their graded modules. And just as modules can be studied by considering their various envelopes and coverings, graded modules can be studied using the graded counterpart of these notions. Graded torsion and graded torsion free modules often arise in the study of projective geometry. Artin and Zhang [2] use graded torsion and graded torsion free modules in their discussion of noncommutative projective varieties. It is known that a module over an integral domain has a unique torsion free covering [1]. In this paper, we initiate the study of graded torsion free, graded divisible, and graded injective modules over the (graded) integral domain k[x] (where k is a field).","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"4 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82077753","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}
引用次数: 0
Relative finitistic projective and injective dimensions 相对有限的射影维和内射维
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2023-01-01 DOI: 10.12988/ija.2023.91758
Y. Wei, Xi Tang
{"title":"Relative finitistic projective and injective dimensions","authors":"Y. Wei, Xi Tang","doi":"10.12988/ija.2023.91758","DOIUrl":"https://doi.org/10.12988/ija.2023.91758","url":null,"abstract":"P.R","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"13 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84637525","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}
引用次数: 0
Solutions to systems of rectangular linear equations mxn, m<n 矩形线性方程组的解mxn, m&lt;n
2区 数学
International Journal of Algebra and Computation Pub Date : 2023-01-01 DOI: 10.12988/ija.2023.91845
E. Salinas-Hernandez, Cesar R. Martinez-Garcia, Jesus A. Martinez-Nuno, M. Abel Leon-Hernandez
{"title":"Solutions to systems of rectangular linear equations mxn, m&lt;n","authors":"E. Salinas-Hernandez, Cesar R. Martinez-Garcia, Jesus A. Martinez-Nuno, M. Abel Leon-Hernandez","doi":"10.12988/ija.2023.91845","DOIUrl":"https://doi.org/10.12988/ija.2023.91845","url":null,"abstract":"As a different alternative to the well established theory to solve systems of rectangular equations","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135211055","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}
引用次数: 0
Four dimensional absolute valued algebras containing a nonzero idempotent commuting with all idempotents 包含与所有幂等元交换的非零幂等元的四维绝对值代数
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2023-01-01 DOI: 10.12988/ija.2023.91757
A. Moutassim, Mohamed Mohamed Louzari, Aziz Es. Sadiq
{"title":"Four dimensional absolute valued algebras containing a nonzero idempotent commuting with all idempotents","authors":"A. Moutassim, Mohamed Mohamed Louzari, Aziz Es. Sadiq","doi":"10.12988/ija.2023.91757","DOIUrl":"https://doi.org/10.12988/ija.2023.91757","url":null,"abstract":"In [9], we have proven that if A is a four-dimensional absolute valued algebra having two different subalgebras isomorphic to C , then A is isomorphic to H , M 1 , M 2 or M 3 . Here we complete the study of A . Indeed, we show if A has two different subalgebras isomorphic to ∗ C . Then A is isomorphic to ∗ H , ∗ M 1 , ∗ M 2 or ∗ M 3 . Furthermore, we classify all four-dimensional absolute valued algebras containing a nonzero idempotent commuting with all idempotents, such an algebra A contains at least two different subalgebras isomorphic to ∗ C . Which means that A is isomorphic to ∗ H , ∗ M 1 , ∗ M 2 or ∗ M 3 .","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"94 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82449752","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}
引用次数: 0
Reduced Cramer's rule 简化克莱默规则
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2023-01-01 DOI: 10.12988/ija.2023.91795
E. Salinas-Hernández, M. A. Leon-Hernandez, Cesar R. Martinez-Garcia, J. A. Martinez-Nuno
{"title":"Reduced Cramer's rule","authors":"E. Salinas-Hernández, M. A. Leon-Hernandez, Cesar R. Martinez-Garcia, J. A. Martinez-Nuno","doi":"10.12988/ija.2023.91795","DOIUrl":"https://doi.org/10.12988/ija.2023.91795","url":null,"abstract":"In this work, starting from the generalized cross product","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"27 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82315484","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}
引用次数: 0
Radicals of an ordered semigroup in terms of type of ordered semigroups 用有序半群的类型表示有序半群的根
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2023-01-01 DOI: 10.12988/ija.2023.91736
M. Tsingelis
{"title":"Radicals of an ordered semigroup in terms of type of ordered semigroups","authors":"M. Tsingelis","doi":"10.12988/ija.2023.91736","DOIUrl":"https://doi.org/10.12988/ija.2023.91736","url":null,"abstract":"A type F of ordered semigroups is a class of ordered semigroups such that (i) if S belongs to F and S  is isomorphic to S, then S  belongs to F , and (ii) any one-element (ordered) semigroup belongs to F . Given a type F of ordered semigroups and an ordered semigroup S, the radS  F is the intersection of all pseudoorders of S having type F (a pseudoorder σ on S has type F if the quotient semigroup of S by the congruence 1 :       has also type F - we consider the quotient semigroup as an ordered semigroup under the induced order relation by σ). The derived type  F of F is the class of all ordered semigroups S such that radS  F is the order relation of S. An F maximal homomorphic image of an ordered semigroup of an ordered semigroup S is an ordered semigroup S  in F for which there exists a homomorphism η of S onto S  with the factorization property: if υ is a homomorphism of S onto an ordered semigroup of type F , then there exists a homomorphism θ of S  onto T such that      . We give sufficient and necessary condition under which an ordered semigroup admits an F maximal homomorphic image. We show that every ordered semigroup has an  F maximal homomorphic image and finally for a type F of ordered semigroups we prove thatevery ordered semigroup has an F maximal homomorphic image if and only if","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73706759","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}
引用次数: 0
On derivatives of eigenvalues, eigenvectors and generalized eigenvectors of matrices 关于矩阵的特征值、特征向量和广义特征向量的导数
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2023-01-01 DOI: 10.12988/ija.2023.91740
N. Yener
{"title":"On derivatives of eigenvalues, eigenvectors and generalized eigenvectors of matrices","authors":"N. Yener","doi":"10.12988/ija.2023.91740","DOIUrl":"https://doi.org/10.12988/ija.2023.91740","url":null,"abstract":"The classical linear eigenvalue problem is considered for matrices whose elements are dependent on a single real variable. Explicit expressions for derivatives of the eiegnvalues and eigenvectors are given in cases of simple and multiple eigenvalues. Recursion relations are obtained for derivatives of consecutively indexed generalized eigenvectors. Particular emphasis is placed on derivatives of eigenvectors and generalized eigenvectors to which enough coverage has not yet been provided in the present day literature.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"68 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84097733","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}
引用次数: 0
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