Pub Date : 2024-08-05DOI: 10.1080/00927872.2024.2377811
Baian Liu
For a domain D, the ring Int(D) of integer-valued polynomials over D is atomic if D satisfies the ascending chain condition on principal ideals. However, even for a discrete valuation domain V, the...
对于一个域 D，如果 D 满足主理想的上升链条件，则 D 上的整数值多项式环 Int(D) 是原子环。然而，即使对于离散估值域 V，...
{"title":"Factorization in rings of integer-valued rational functions","authors":"Baian Liu","doi":"10.1080/00927872.2024.2377811","DOIUrl":"https://doi.org/10.1080/00927872.2024.2377811","url":null,"abstract":"For a domain D, the ring Int(D) of integer-valued polynomials over D is atomic if D satisfies the ascending chain condition on principal ideals. However, even for a discrete valuation domain V, the...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"34 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-05DOI: 10.1080/00927872.2024.2382813
Dongfang Yang, Yu Zeng
We define, and denote by anz(G), the average number of zeros of characters of a finite group G as the number of zeros in the character table of G dividing the number of irreducible characters of G....
我们将有限群 G 的平均字符零点数定义为 G 字符表中的零点数除以 G 的不可还原字符数，并用 anz(G) 表示....。
{"title":"Odd-order groups with small average number of zeros of characters","authors":"Dongfang Yang, Yu Zeng","doi":"10.1080/00927872.2024.2382813","DOIUrl":"https://doi.org/10.1080/00927872.2024.2382813","url":null,"abstract":"We define, and denote by anz(G), the average number of zeros of characters of a finite group G as the number of zeros in the character table of G dividing the number of irreducible characters of G....","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"198 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-02DOI: 10.1080/00927872.2024.2381825
Hossein Faridian
We prove that if f:R→S is a local homomorphism of noetherian local rings, and M is a non-zero finitely generated or artinian S-module whose injective dimension over R is bounded by the difference ...
{"title":"Bounds on injective dimension and exceptional complete intersection maps","authors":"Hossein Faridian","doi":"10.1080/00927872.2024.2381825","DOIUrl":"https://doi.org/10.1080/00927872.2024.2381825","url":null,"abstract":"We prove that if f:R→S is a local homomorphism of noetherian local rings, and M is a non-zero finitely generated or artinian S-module whose injective dimension over R is bounded by the difference ...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"30 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-02DOI: 10.1080/00927872.2024.2379488
Sunil Kumar Prajapati, Ayush Udeep
For a finite group G, we denote by c(G) , the minimal degree of a faithful representation of G by quasi-permutation matrices over C . For an irreducible character χ of G, the codegree of χ is def...
对于有限群 G，我们用 c(G)表示 G 在 C 上的准互变矩阵忠实表示的最小度。对于 G 的不可还原特性 χ，χ 的度数定义为...
{"title":"On the relation of character codegrees and the minimal faithful quasi-permutation representation degree of p-groups","authors":"Sunil Kumar Prajapati, Ayush Udeep","doi":"10.1080/00927872.2024.2379488","DOIUrl":"https://doi.org/10.1080/00927872.2024.2379488","url":null,"abstract":"For a finite group G, we denote by c(G) , the minimal degree of a faithful representation of G by quasi-permutation matrices over C . For an irreducible character χ of G, the codegree of χ is def...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-01DOI: 10.1080/00927872.2024.2373374
David Meretzky, Anand Pillay
Let K be a differential field with algebraically closed field of constants CK. Let KPV∞ be the (iterated) Picard-Vessiot closure of K. Let G be a linear differential algebraic group over K, and X a...
设 K 是一个微分域，其常量代数闭域为 CK。设 KPV∞ 是 K 的（迭代）皮卡尔-维西奥封闭。
{"title":"Picard-Vessiot extensions, linear differential algebraic groups, and their torsors","authors":"David Meretzky, Anand Pillay","doi":"10.1080/00927872.2024.2373374","DOIUrl":"https://doi.org/10.1080/00927872.2024.2373374","url":null,"abstract":"Let K be a differential field with algebraically closed field of constants CK. Let KPV∞ be the (iterated) Picard-Vessiot closure of K. Let G be a linear differential algebraic group over K, and X a...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"41 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-01DOI: 10.1080/00927872.2024.2377390
Nicolae Ciprian Bonciocat, Rishu Garg, Jitender Singh
We provide upper bounds on the total number of irreducible factors, and in particular irreducibility criteria for some classes of bivariate polynomials f(x, y) over an arbitrary field K. Our result...
我们为任意域 K 上的一些二元多项式 f(x, y) 提供了不可还原因子总数的上限，特别是不可还原性标准。
{"title":"Some factorization results for bivariate polynomials","authors":"Nicolae Ciprian Bonciocat, Rishu Garg, Jitender Singh","doi":"10.1080/00927872.2024.2377390","DOIUrl":"https://doi.org/10.1080/00927872.2024.2377390","url":null,"abstract":"We provide upper bounds on the total number of irreducible factors, and in particular irreducibility criteria for some classes of bivariate polynomials f(x, y) over an arbitrary field K. Our result...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"26 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-29DOI: 10.1080/00927872.2024.2369906
William Bernardoni
We introduce a generalization of the universal valuation semiring defined by Jeffrey and Noah Giansiracusa. We then explicitly characterize the additive structure of this semiring and show that, wh...
{"title":"Applications of generalized universal valuations","authors":"William Bernardoni","doi":"10.1080/00927872.2024.2369906","DOIUrl":"https://doi.org/10.1080/00927872.2024.2369906","url":null,"abstract":"We introduce a generalization of the universal valuation semiring defined by Jeffrey and Noah Giansiracusa. We then explicitly characterize the additive structure of this semiring and show that, wh...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"373 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-23DOI: 10.1080/00927872.2024.2374430
Dilpreet Kaur, Pushpendra Singh
Let C be field of complex numbers and X be a connected quandle of prime order. We study the regular representation of X by describing the quandle ring C[X] as direct sum of right simple ideals. W...
设 C 是复数域，X 是素阶相连的 quandle。我们研究 X 的正则表达式，将 quandle 环 C[X] 描述为右简单理想的直和。W...
{"title":"Tensor product and quandle rings of connected quandles of prime order","authors":"Dilpreet Kaur, Pushpendra Singh","doi":"10.1080/00927872.2024.2374430","DOIUrl":"https://doi.org/10.1080/00927872.2024.2374430","url":null,"abstract":"Let C be field of complex numbers and X be a connected quandle of prime order. We study the regular representation of X by describing the quandle ring C[X] as direct sum of right simple ideals. W...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"80 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-22DOI: 10.1080/00927872.2024.2371559
Jingwen Shen, Xiaoyan Yang
Let R be a commutative noetherian ring and a an ideal of R. The goal of this paper is to establish the local-global principle for the artinianness dimension ra(M), where ra(M) is the smallest integ...
{"title":"The local-global principle for the artinianness dimensions","authors":"Jingwen Shen, Xiaoyan Yang","doi":"10.1080/00927872.2024.2371559","DOIUrl":"https://doi.org/10.1080/00927872.2024.2371559","url":null,"abstract":"Let R be a commutative noetherian ring and a an ideal of R. The goal of this paper is to establish the local-global principle for the artinianness dimension ra(M), where ra(M) is the smallest integ...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"81 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-22DOI: 10.1080/00927872.2024.2376861
Yue Li, Yanyong Hong
Pre-Novikov algebras and quasi-Frobenius Novikov algebras naturally appear in the theory of Novikov bialgebras. In this paper, we show that there is a natural pre-Novikov algebra structure associat...
{"title":"Quasi-Frobenius Novikov algebras and pre-Novikov bialgebras","authors":"Yue Li, Yanyong Hong","doi":"10.1080/00927872.2024.2376861","DOIUrl":"https://doi.org/10.1080/00927872.2024.2376861","url":null,"abstract":"Pre-Novikov algebras and quasi-Frobenius Novikov algebras naturally appear in the theory of Novikov bialgebras. In this paper, we show that there is a natural pre-Novikov algebra structure associat...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"39 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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