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International Journal of Algebra and Computation最新文献

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A remark on arithmetical rings 关于算术环的注解
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2021-01-01 DOI: 10.12988/ija.2021.91575
Majid M. Ali
{"title":"A remark on arithmetical rings","authors":"Majid M. Ali","doi":"10.12988/ija.2021.91575","DOIUrl":"https://doi.org/10.12988/ija.2021.91575","url":null,"abstract":"ΦA,B := {I | I is non-zero finitely generated, A ⊆ I, I + B = R} . He showed, [3, Theorem 5], that M is the smallest element in ΦA,B if and only if the following conditions are satisfied: ( i) A ⊆ M , ( ii) M + B = R and ( iii) if S is a non-zero a finitely generated ideal in R such that AM−1 ⊆ S and S + B = R, then R = S. He also proved, [3, Corollary to Theorem 4], that the smallest element always exists if R is a Dedekind domain. In this short note we generalize these two results to arithmetical rings. Recall that a ring R is called an arithmetical ring if every finitely generated ideal in R is multiplication. An ideal A in R is multiplication if for every ideal B ⊆ A, there exists an ideal C in R such that B = CA, [2]. Note that C ⊆ [B : A], and hence B = CA ⊆ [B : A]A ⊆ B,","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"33 5 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78248470","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
Characterization of pure Hurwitz numbers 纯Hurwitz数的表征
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2021-01-01 DOI: 10.12988/IJA.2021.91530
J. Rodriguez, V. Bautista-Ancona
{"title":"Characterization of pure Hurwitz numbers","authors":"J. Rodriguez, V. Bautista-Ancona","doi":"10.12988/IJA.2021.91530","DOIUrl":"https://doi.org/10.12988/IJA.2021.91530","url":null,"abstract":"We explore the nature of the continued fraction expansion of the Hurwitz numbers H = (ae2/n + b)/(ce2/n + d), with D = |ad− bc| 6 = 0. We prove some results for determinant pk with p a prime number. Also, we conjecture families of ‘pure’ Hurwitz numbers with determinant 2. Mathematics Subject Classification: 11A55, 11J70","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"44 1","pages":"111-122"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73528043","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
Group-like Small Cancellation Theory for Rings 环的类群小消去理论
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2020-10-06 DOI: 10.1142/s0218196723500522
A. Atkarskaya, A. Kanel-Belov, E. Plotkin, E. Rips
{"title":"Group-like Small Cancellation Theory for Rings","authors":"A. Atkarskaya, A. Kanel-Belov, E. Plotkin, E. Rips","doi":"10.1142/s0218196723500522","DOIUrl":"https://doi.org/10.1142/s0218196723500522","url":null,"abstract":"In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding defining relations. We show that the obtained ring is non-trivial. Moreover, we show that this ring enjoys a global filtration that agrees with relations, find a basis of the ring as a vector space and establish the corresponding structure theorems. We also provide a revision of a concept of Grobner basis for our rings and establish a greedy algorithm for the Ideal Membership Problem.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48327510","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: 2
On Fuzzy Quasi-Invex Sets 关于模糊拟逆集
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2020-08-23 DOI: 10.20454/IJAS.2020.1613
Muhammad Bilal Khan, M. Noor, K. Noor
{"title":"On Fuzzy Quasi-Invex Sets","authors":"Muhammad Bilal Khan, M. Noor, K. Noor","doi":"10.20454/IJAS.2020.1613","DOIUrl":"https://doi.org/10.20454/IJAS.2020.1613","url":null,"abstract":"This study aims to consider new kind of a set is called fuzzy quasi-invex set, which is convenient to handle real world application like optimization problems. And it investigates fuzzy quasi-convex set in view of new set. Some examples are given to illustrate that Zadeh’s fuzzy quasi-convex set and classical convex set are special cases of fuzzy quasi-invex set. It is also proved that classical invex sets are fuzzy quasi-invex set. Further, some properties of fuzzy quasi-invex set are investigated and generalized in term of generalized fuzzy quasi-invex set. Furthermore, some properties of fuzzy optimizations are discussed.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"29 1","pages":"11-26"},"PeriodicalIF":0.8,"publicationDate":"2020-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77928039","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: 3
Numerical semigroups of small and large type 大小型的数值半群
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2020-08-18 DOI: 10.1142/S0218196721500417
Deepesh Singhal
{"title":"Numerical semigroups of small and large type","authors":"Deepesh Singhal","doi":"10.1142/S0218196721500417","DOIUrl":"https://doi.org/10.1142/S0218196721500417","url":null,"abstract":"A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. Some of the key properties of a numerical semigroup are its Frobenius number [Formula: see text], genus [Formula: see text] and type [Formula: see text]. It is known that for any numerical semigroup [Formula: see text]. Numerical semigroups with [Formula: see text] are called almost symmetric, we introduce a new property that characterizes them. We give an explicit characterization of numerical semigroups with [Formula: see text]. We show that for a fixed [Formula: see text] the number of numerical semigroups with Frobenius number [Formula: see text] and type [Formula: see text] is eventually constant for large [Formula: see text]. The number of numerical semigroups with genus [Formula: see text] and type [Formula: see text] is also eventually constant for large [Formula: see text].","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"31 1","pages":"883-902"},"PeriodicalIF":0.8,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63937064","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
Center of skew PBW extensions 倾斜PBW扩展中心
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2020-08-07 DOI: 10.1142/S0218196720500575
O. Lezama, Helbert Venegas
{"title":"Center of skew PBW extensions","authors":"O. Lezama, Helbert Venegas","doi":"10.1142/S0218196720500575","DOIUrl":"https://doi.org/10.1142/S0218196720500575","url":null,"abstract":"In this paper we compute the center of many noncommutative algebras that can be interpreted as skew PBW extensions. We show that, under some natural assumptions on the parameters that define the ex...","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"30 1","pages":"1625-1650"},"PeriodicalIF":0.8,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0218196720500575","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63937018","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
Enumeraion in ranks of various elliptic curves y2 = x3 ∓ AX 各种椭圆曲线的秩数y2 = x3 - AX
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2020-01-01 DOI: 10.12988/ija.2020.91250
Shin-wook Kim
{"title":"Enumeraion in ranks of various elliptic curves y2 = x3 ∓ AX","authors":"Shin-wook Kim","doi":"10.12988/ija.2020.91250","DOIUrl":"https://doi.org/10.12988/ija.2020.91250","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"43 1","pages":"139-162"},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89634832","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: 4
Prime LI-ideal spaces of MTL-algebras mtl代数的素li -理想空间
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2020-01-01 DOI: 10.12988/ija.2020.91259
Chunhui Liu, Luoshan Xu
{"title":"Prime LI-ideal spaces of MTL-algebras","authors":"Chunhui Liu, Luoshan Xu","doi":"10.12988/ija.2020.91259","DOIUrl":"https://doi.org/10.12988/ija.2020.91259","url":null,"abstract":"In this paper, topological spaces based on prime LI -ideals and on maximal LI -ideals of an MTL-algebra are constructed. It is proved that the topological spaces constructed on LI -ideals are compact T0spaces and that the topological spaces constructed on maximal LI -ideals are compact T2-spaces. These give interactions between Non-Classical Mathematical Logic and General Topology. Mathematics Subject Classifications: 03G10; 54D40; 08A72","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"56 1","pages":"213-222"},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85945936","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
Properties and characterizations of ν-C-continuous posets ν- c -连续序集的性质与表征
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2020-01-01 DOI: 10.12988/ija.2020.91271
Xuxin Mao, Luoshan Xu
{"title":"Properties and characterizations of ν-C-continuous posets","authors":"Xuxin Mao, Luoshan Xu","doi":"10.12988/ija.2020.91271","DOIUrl":"https://doi.org/10.12988/ija.2020.91271","url":null,"abstract":"In this paper, for a fixed cardinal ν, the concept of ν-C-continuous posets is introduced. Properties and characterizations of ν-C-continuous posets are presented. The main results are: (1) The lattice of all ν-Scottclosed subsets for a poset is a ν-C-continuous lattice; (2) A complete lattice is a completely distributive lattice iff it is ν-C-continuous and ν-continuous. Mathematics Subject Classifications: 06A11; 06B35; 54C35; 54D45","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"54 1","pages":"223-231"},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83573611","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
A brief note on absolute valued algebras with involution 关于有对合的绝对值代数的简要说明
IF 0.8 2区 数学
International Journal of Algebra and Computation Pub Date : 2020-01-01 DOI: 10.12988/ija.2020.91279
O. Fayz, A. Rochdi
{"title":"A brief note on absolute valued algebras with involution","authors":"O. Fayz, A. Rochdi","doi":"10.12988/ija.2020.91279","DOIUrl":"https://doi.org/10.12988/ija.2020.91279","url":null,"abstract":"We give some necessary and sufficient conditions giving rise to the finite dimensionality of any absolute-valued algebra with involution. Mathematics Subject Classification: 17A35, 17A80","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"43 1","pages":"297-301"},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73838179","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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