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Brauer–Clifford Group of Lie–Rinehart Algebras Lie-Rinehart代数的Brauer-Clifford群
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2022-01-13 DOI: 10.1142/s1005386722000086
T. Guédénon
{"title":"Brauer–Clifford Group of Lie–Rinehart Algebras","authors":"T. Guédénon","doi":"10.1142/s1005386722000086","DOIUrl":"https://doi.org/10.1142/s1005386722000086","url":null,"abstract":"In this paper we define the notion of Brauer–Clifford group for [Formula: see text]-Azumaya algebras when [Formula: see text] is a commutative algebra and[Formula: see text] is a [Formula: see text]-Lie algebra over a commutative ring [Formula: see text]. This is the situation that arises in applications having connections to differential geometry. This Brauer–Clifford group turns out to be an example of a Brauer group of a symmetric monoidal category.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81091275","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 Existence of Primitive Normal Elements of Cubic Form over Finite Fields 有限域上三次型原始正规元的存在性
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2022-01-13 DOI: 10.1142/s1005386722000128
H. Hazarika, D. Basnet
{"title":"On Existence of Primitive Normal Elements of Cubic Form over Finite Fields","authors":"H. Hazarika, D. Basnet","doi":"10.1142/s1005386722000128","DOIUrl":"https://doi.org/10.1142/s1005386722000128","url":null,"abstract":"For a prime [Formula: see text]and a positive integer[Formula: see text], let [Formula: see text] and [Formula: see text] be the extension field of [Formula: see text]. We derive a sufficient condition for the existence of a primitive element [Formula: see text] in[Formula: see text] such that [Formula: see text] is also a primitive element of [Formula: see text], a sufficient condition for the existence of a primitive normal element [Formula: see text] in [Formula: see text] over [Formula: see text] such that [Formula: see text] is a primitive element of [Formula: see text], and a sufficient condition for the existence of a primitive normal element [Formula: see text] in [Formula: see text] over [Formula: see text] such that [Formula: see text] is also a primitive normal element of [Formula: see text] over [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87906851","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
Open Frobenius Cluster-Tilted Algebras 开放Frobenius簇-倾斜代数
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2022-01-13 DOI: 10.1142/S1005386722000025
Viviana Gubitosi
{"title":"Open Frobenius Cluster-Tilted Algebras","authors":"Viviana Gubitosi","doi":"10.1142/S1005386722000025","DOIUrl":"https://doi.org/10.1142/S1005386722000025","url":null,"abstract":"In this paper, we compute the Frobenius dimension of any cluster-tilted algebra of finite type. Moreover, we give conditions on the bound quiver of a cluster-tilted algebra [Formula: see text] such that [Formula: see text] has non-trivial open Frobenius structures.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75266380","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
Classical Radicals of Invariants of Algebraic Skew Derivations 代数偏导的不变量的经典根
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2022-01-13 DOI: 10.1142/s1005386722000050
Jeffrey Bergen, Piotr Grzeszczuk
{"title":"Classical Radicals of Invariants of Algebraic Skew Derivations","authors":"Jeffrey Bergen, Piotr Grzeszczuk","doi":"10.1142/s1005386722000050","DOIUrl":"https://doi.org/10.1142/s1005386722000050","url":null,"abstract":"Let [Formula: see text] be an automorphism and[Formula: see text] be a [Formula: see text]-skew [Formula: see text]-derivation of an [Formula: see text]-algebra [Formula: see text]. We prove that if [Formula: see text] is semiprimitive and [Formula: see text] is algebraic, then the subalgebra [Formula: see text] has nilpotent Jacobson radical. Using this result, we obtain similar relations for the Baer prime radical, the Levitzki locally nilpotent radical, and the Köthe nil radical when the field [Formula: see text] is uncountable. Then we apply it to actions of the [Formula: see text]-dimensional Taft Hopf algebra [Formula: see text] and the [Formula: see text]-analogue [Formula: see text] of the enveloping algebra of the Lie algebra [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84921128","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 Finite Local Rings with Clique Number Four 团数为4的有限局部环上
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2022-01-13 DOI: 10.1142/s1005386722000037
Qiong Liu, Tongsuo Wu, Jin Guo
{"title":"On Finite Local Rings with Clique Number Four","authors":"Qiong Liu, Tongsuo Wu, Jin Guo","doi":"10.1142/s1005386722000037","DOIUrl":"https://doi.org/10.1142/s1005386722000037","url":null,"abstract":"We study the algebraic structure of rings [Formula: see text] whose zero-divisor graph [Formula: see text]has clique number four. Furthermore, we give complete characterizations of all the finite commutative local rings with clique number 4.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83454635","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 Results on Noetherian Warfield Domains 关于Noetherian Warfield域的一些结果
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2022-01-13 DOI: 10.1142/s1005386722000062
Kui Hu, J. Lim, D. Zhou
{"title":"Some Results on Noetherian Warfield Domains","authors":"Kui Hu, J. Lim, D. Zhou","doi":"10.1142/s1005386722000062","DOIUrl":"https://doi.org/10.1142/s1005386722000062","url":null,"abstract":"Let [Formula: see text] be a domain. In this paper, we show that if [Formula: see text] is one-dimensional, then [Formula: see text] is a Noetherian Warfield domain if and only if every maximal ideal of [Formula: see text] is 2-generated and for every maximal ideal[Formula: see text] of [Formula: see text], [Formula: see text] is divisorial in the ring [Formula: see text]. We also prove that a Noetherian domain [Formula: see text] is a Noetherian Warfield domain if and only if for every maximal ideal [Formula: see text] of [Formula: see text], [Formula: see text] can be generated by two elements. Finally, we give a sufficient condition under which all ideals of [Formula: see text] are strongly Gorenstein projective.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87328773","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
Three Ideals of Lie Superalgebras 李超代数的三个理想
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2022-01-13 DOI: 10.1142/s1005386722000116
Xiaodong Zhao, Liangyun Chen
{"title":"Three Ideals of Lie Superalgebras","authors":"Xiaodong Zhao, Liangyun Chen","doi":"10.1142/s1005386722000116","DOIUrl":"https://doi.org/10.1142/s1005386722000116","url":null,"abstract":"We define perfect ideals, near perfect ideals and upper bounded ideals of a finite-dimensional Lie superalgebra, and study the properties of these three kinds of ideals through their relevant sequences. We prove that a Lie superalgebra is solvable if and only if its maximal perfect ideal is zero, or its quotient superalgebra by the maximal perfect ideal is solvable. We also show that a Lie superalgebra is nilpotent if and only if its maximal near perfect ideal is zero. Moreover, we prove that a nilpotent Lie superalgebra has only one upper bounded ideal, which is the nilpotent Lie superalgebra itself.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78505296","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
One-Generated Nilpotent Bicommutative Algebras 单生成幂零双交换代数
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-12-01 DOI: 10.1142/S1005386722000359
I. Kaygorodov, Pilar P'aez-Guill'an, Vasily Voronin
{"title":"One-Generated Nilpotent Bicommutative Algebras","authors":"I. Kaygorodov, Pilar P'aez-Guill'an, Vasily Voronin","doi":"10.1142/S1005386722000359","DOIUrl":"https://doi.org/10.1142/S1005386722000359","url":null,"abstract":"We give a classification of 5- and 6-dimensional complex one-generated nilpotent bicommutative algebras.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86597269","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
On Ordinary Words of Standard Reed–Solomon Codes over Finite Fields 有限域上标准Reed-Solomon码的常用词
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-11-08 DOI: 10.1142/s1005386721000456
Xiaofang Xu, Shaofang Hong
{"title":"On Ordinary Words of Standard Reed–Solomon Codes over Finite Fields","authors":"Xiaofang Xu, Shaofang Hong","doi":"10.1142/s1005386721000456","DOIUrl":"https://doi.org/10.1142/s1005386721000456","url":null,"abstract":"Reed–Solomon codes are widely used to establish a reliable channel to transmit information in digital communication which has a strong error correction capability and a variety of efficient decoding algorithm. Usually we use the maximum likelihood decoding (MLD) algorithm in the decoding process of Reed–Solomon codes. MLD algorithm relies on determining the error distance of received word. Dür, Guruswami, Wan, Li, Hong, Wu, Yue and Zhu et al. got some results on the error distance. For the Reed–Solomon code [Formula: see text], the received word [Formula: see text] is called an ordinary word of [Formula: see text] if the error distance [Formula: see text] with [Formula: see text] being the Lagrange interpolation polynomial of [Formula: see text]. We introduce a new method of studying the ordinary words. In fact, we make use of the result obtained by Y.C. Xu and S.F. Hong on the decomposition of certain polynomials over the finite field to determine all the ordinary words of the standard Reed–Solomon codes over the finite field of [Formula: see text] elements. This completely answers an open problem raised by Li and Wan in [On the subset sum problem over finite fields, Finite Fields Appl. 14 (2008) 911–929].","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":"89979658","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
Coleman Automorphisms of Extensions of Finite Characteristically Simple Groups by Some Finite Groups 有限特征单群被某些有限群扩展的Coleman自同构
IF 0.3 4区 数学
Algebra Colloquium Pub Date : 2021-11-08 DOI: 10.1142/s1005386721000444
J. Hai, Lele Zhao
{"title":"Coleman Automorphisms of Extensions of Finite Characteristically Simple Groups by Some Finite Groups","authors":"J. Hai, Lele Zhao","doi":"10.1142/s1005386721000444","DOIUrl":"https://doi.org/10.1142/s1005386721000444","url":null,"abstract":"Let [Formula: see text] be an extension of a finite characteristically simple group by an abelian group or a finite simple group. It is shown that every Coleman automorphism of [Formula: see text] is an inner automorphism. Interest in such automorphisms arises from the study of the normalizer problem for integral group rings.","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":"76563576","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
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