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Arc-Transitive Graphs of Square-free Order with Valency 11 价为11的无平方阶弧传递图
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-11-08 DOI: 10.1142/s100538672100050x
Guangnuan Li, B. Ling, Z. Lu
{"title":"Arc-Transitive Graphs of Square-free Order with Valency 11","authors":"Guangnuan Li, B. Ling, Z. Lu","doi":"10.1142/s100538672100050x","DOIUrl":"https://doi.org/10.1142/s100538672100050x","url":null,"abstract":"In this paper, we present a complete list of connected arc-transitive graphs of square-free order with valency 11. The list includes the complete bipartite graph [Formula: see text], the normal Cayley graphs of dihedral groups and the graphs associated with the simple group [Formula: see text] and [Formula: see text], where [Formula: see text] is a prime.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73922835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Ideal-Based k-Zero-Divisor Hypergraph of Commutative Rings 交换环的基于理想的k-零因子超图
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-11-08 DOI: 10.1142/s1005386721000511
K. Selvakumar, M. Subajini
{"title":"Ideal-Based k-Zero-Divisor Hypergraph of Commutative Rings","authors":"K. Selvakumar, M. Subajini","doi":"10.1142/s1005386721000511","DOIUrl":"https://doi.org/10.1142/s1005386721000511","url":null,"abstract":"Let [Formula: see text] be a commutative ring, [Formula: see text] an ideal of [Formula: see text] and [Formula: see text] a fixed integer. The ideal-based [Formula: see text]-zero-divisor hypergraph [Formula: see text] of [Formula: see text] has vertex set [Formula: see text], the set of all ideal-based [Formula: see text]-zero-divisors of [Formula: see text], and for distinct elements [Formula: see text] in [Formula: see text], the set [Formula: see text] is an edge in [Formula: see text] if and only if [Formula: see text] and the product of the elements of any [Formula: see text]-subset of [Formula: see text] is not in [Formula: see text]. In this paper, we show that [Formula: see text] is connected with diameter at most 4 provided that [Formula: see text] for all ideal-based 3-zero-divisor hypergraphs. Moreover, we find the chromatic number of [Formula: see text] when [Formula: see text] is a product of finite fields. Finally, we find some necessary conditions for a finite ring [Formula: see text] and a nonzero ideal [Formula: see text] of [Formula: see text] to have [Formula: see text] planar.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85354587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Some Kazhdan–Lusztig Coefficients of Affine Weyl Group of Type B~ 2 B~ 2型仿射Weyl群的Kazhdan-Lusztig系数
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-11-08 DOI: 10.1142/s1005386721000420
Ge Feng, Liping Wang
{"title":"Some Kazhdan–Lusztig Coefficients of Affine Weyl Group of Type B~ 2","authors":"Ge Feng, Liping Wang","doi":"10.1142/s1005386721000420","DOIUrl":"https://doi.org/10.1142/s1005386721000420","url":null,"abstract":"Let [Formula: see text] be the affine Weyl group of type [Formula: see text], on which we consider the length function [Formula: see text] from [Formula: see text] to [Formula: see text] and the Bruhat order [Formula: see text]. For [Formula: see text] in [Formula: see text], let [Formula: see text] be the coefficient of [Formula: see text] in Kazhdan–Lusztig polynomial [Formula: see text]. We determine some [Formula: see text] for [Formula: see text] and [Formula: see text], where [Formula: see text] is the lowest two-sided cell of [Formula: see text] and [Formula: see text] is the higher one. Furthermore, we get some consequences using left or right strings and some properties of leading coefficients.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85235731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 the Generalized Strongly Nil-Clean Property of Matrix Rings 关于矩阵环的广义强Nil-Clean性质
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-11-08 DOI: 10.1142/s1005386721000481
A. Kostic, Z. Petrovic, Zoran S. Pucanovic, Maja Roslavcev
{"title":"On the Generalized Strongly Nil-Clean Property of Matrix Rings","authors":"A. Kostic, Z. Petrovic, Zoran S. Pucanovic, Maja Roslavcev","doi":"10.1142/s1005386721000481","DOIUrl":"https://doi.org/10.1142/s1005386721000481","url":null,"abstract":"Let [Formula: see text] be an associative unital ring and not necessarily commutative. We analyze conditions under which every [Formula: see text] matrix [Formula: see text] over [Formula: see text] is expressible as a sum [Formula: see text] of (commuting) idempotent matrices [Formula: see text] and a nilpotent matrix [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91107233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Note on the Universal Factorization Property of Groups 关于群的全称分解性质的注记
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-11-08 DOI: 10.1142/s1005386721000493
Injo Hur, J. Jo
{"title":"A Note on the Universal Factorization Property of Groups","authors":"Injo Hur, J. Jo","doi":"10.1142/s1005386721000493","DOIUrl":"https://doi.org/10.1142/s1005386721000493","url":null,"abstract":"We give criteria when a full subcategory [Formula: see text] of the category of groups has [Formula: see text]-universal factorization property ([Formula: see text]-UFP) or [Formula: see text]-strong universal factorization property ([Formula: see text]-SUFP) for a certain category of groups [Formula: see text]. As a byproduct, we give affirmative answers to three unsettled questions in [S.W. Kim, J.B. Lee, Universal factorization property of certain polycyclic groups, J. Pure Appl. Algebra 204 (2006) 555–567].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88615592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
An Upper Bound for the w-Weak Global Dimension of Pullbacks 回调的w-弱整体维数的上界
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-11-08 DOI: 10.1142/s1005386721000535
Jin Xie, Gaohua Tang
{"title":"An Upper Bound for the w-Weak Global Dimension of Pullbacks","authors":"Jin Xie, Gaohua Tang","doi":"10.1142/s1005386721000535","DOIUrl":"https://doi.org/10.1142/s1005386721000535","url":null,"abstract":"Let [Formula: see text] be a commutative ring with identity and [Formula: see text] an ideal of [Formula: see text]. We introduce and study the [Formula: see text]-weak global dimension [Formula: see text] of the factor ring [Formula: see text]. Let [Formula: see text] be a [Formula: see text]-linked extension of [Formula: see text], and we also introduce the [Formula: see text]-weak global dimension [Formula: see text] of [Formula: see text]. We show that the ring [Formula: see text] with [Formula: see text] is exactly a field and the ring [Formula: see text] with [Formula: see text] is exactly a [Formula: see text]. As an application, we give an upper bound for the [Formula: see text]-weak global dimension of a Cartesian square [Formula: see text]. More precisely, if [Formula: see text] is [Formula: see text]-linked over [Formula: see text], then [Formula: see text]. Furthermore, for a Milnor square [Formula: see text], we obtain [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82623942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Upper and Lower Bounds of Table Sums 表和的上下界
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-11-08 DOI: 10.1142/s1005386721000432
Xiaoyou Chen, M. Lewis, H. Tong-Viet
{"title":"Upper and Lower Bounds of Table Sums","authors":"Xiaoyou Chen, M. Lewis, H. Tong-Viet","doi":"10.1142/s1005386721000432","DOIUrl":"https://doi.org/10.1142/s1005386721000432","url":null,"abstract":"For a group [Formula: see text], we produce upper and lower bounds for the sum of the entries of the Brauer character table of [Formula: see text] and the projective indecomposable character table of [Formula: see text]. When [Formula: see text] is a [Formula: see text]-separable group, we show that the sum of the entries in the table of Isaacs' partial characters is a real number, and we obtain upper and lower bounds for this sum.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79611420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Symbol-Pair Distances of Repeated-Root Negacyclic Codes of Length 2s over Galois Rings 伽罗瓦环上长度为2s的重根负环码的符号对距离
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-11-08 DOI: 10.1142/s1005386721000468
H. Dinh, Hualu Liu, R. Tansuchat, Thang M. Vo
{"title":"Symbol-Pair Distances of Repeated-Root Negacyclic Codes of Length 2s over Galois Rings","authors":"H. Dinh, Hualu Liu, R. Tansuchat, Thang M. Vo","doi":"10.1142/s1005386721000468","DOIUrl":"https://doi.org/10.1142/s1005386721000468","url":null,"abstract":"Negacyclic codes of length [Formula: see text] over the Galois ring [Formula: see text] are linearly ordered under set-theoretic inclusion, i.e., they are the ideals [Formula: see text], [Formula: see text], of the chain ring [Formula: see text]. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field [Formula: see text] (i.e., [Formula: see text]), the symbol-pair distance distribution of constacyclic codes over [Formula: see text] verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length [Formula: see text] over [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72456918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On the Inclusion Ideal Graph of Semigroups 关于半群的包含理想图
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-10-27 DOI: 10.1142/s1005386723000342
Barkha Baloda, J. Kumar
{"title":"On the Inclusion Ideal Graph of Semigroups","authors":"Barkha Baloda, J. Kumar","doi":"10.1142/s1005386723000342","DOIUrl":"https://doi.org/10.1142/s1005386723000342","url":null,"abstract":"The inclusion ideal graph [Formula: see text] of a semigroup [Formula: see text] is an undirected simple graph whose vertices are all the nontrivial left ideals of [Formula: see text] and two distinct left ideals [Formula: see text], [Formula: see text] are adjacent if and only if either [Formula: see text] or [Formula: see text]. The purpose of this paper is to study algebraic properties of the semigroup [Formula: see text] as well as graph theoretic properties of [Formula: see text]. We investigate the connectedness of [Formula: see text] and show that the diameter of [Formula: see text] is at most 3 if it is connected. We also obtain a necessary and sufficient condition of [Formula: see text] such that the clique number of [Formula: see text] is the number of minimal left ideals of [Formula: see text]. Further, various graph invariants of [Formula: see text], viz. perfectness, planarity, girth, etc., are discussed. For a completely simple semigroup [Formula: see text], we investigate properties of [Formula: see text] including its independence number and matching number. Finally, we obtain the automorphism group of [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82707261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Balanced Pairs on Triangulated Categories 三角分类上的平衡对
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-09-02 DOI: 10.1142/s1005386723000329
X. Fu, Jiangsheng Hu, Dongdong Zhang, Hai-yan Zhu
{"title":"Balanced Pairs on Triangulated Categories","authors":"X. Fu, Jiangsheng Hu, Dongdong Zhang, Hai-yan Zhu","doi":"10.1142/s1005386723000329","DOIUrl":"https://doi.org/10.1142/s1005386723000329","url":null,"abstract":"Let [Formula: see text] be a triangulated category. We first introduce the notion of balanced pairs in [Formula: see text], and then establish the bijective correspondence between balanced pairs and proper classes [Formula: see text] with enough [Formula: see text]-projectives and [Formula: see text]-injectives. Assume that [Formula: see text] is the proper class induced by a balanced pair [Formula: see text]. We prove that [Formula: see text] is an extriangulated category. Moreover, it is proved that [Formula: see text] is a triangulated category if and only if [Formula: see text], and that [Formula: see text] is an exact category if and only if [Formula: see text]. As an application, we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83443445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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