{"title":"无穷域上Grassmann代数上的n -分级:分级恒等式和中心多项式","authors":"Claudemir Fideles, Alan Guimaraes","doi":"10.1142/s0218196723500650","DOIUrl":null,"url":null,"abstract":"Let [Formula: see text] be the infinite-dimensional Grassmann algebra over an infinite field [Formula: see text] of characteristic different from 2. The main purpose of this paper is to describe the [Formula: see text]-ideal of the graded polynomial identities and the [Formula: see text]-space of the central polynomials of [Formula: see text] equipped with its [Formula: see text] and [Formula: see text]-induced [Formula: see text]-gradings. Therefore, we generalize the results of [A. Brandão, C. Fidelis and A. Guimarães, [Formula: see text]-gradings of full support on the Grassmann algebra, J. Algebra 601 (2022) 332–353; C. Fidelis, A. Guimarães and P. Koshlukov, A note on [Formula: see text]-gradings on the Grassmann algebra and elementary number theory, Linear Multilinear Algebra 71(7) (2023) 1244–1264] in the PI theory context.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" 85","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ℤ-Gradings on the Grassmann Algebra Over Infinite Fields: Graded Identities and Central Polynomials\",\"authors\":\"Claudemir Fideles, Alan Guimaraes\",\"doi\":\"10.1142/s0218196723500650\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let [Formula: see text] be the infinite-dimensional Grassmann algebra over an infinite field [Formula: see text] of characteristic different from 2. The main purpose of this paper is to describe the [Formula: see text]-ideal of the graded polynomial identities and the [Formula: see text]-space of the central polynomials of [Formula: see text] equipped with its [Formula: see text] and [Formula: see text]-induced [Formula: see text]-gradings. Therefore, we generalize the results of [A. Brandão, C. Fidelis and A. Guimarães, [Formula: see text]-gradings of full support on the Grassmann algebra, J. Algebra 601 (2022) 332–353; C. Fidelis, A. Guimarães and P. Koshlukov, A note on [Formula: see text]-gradings on the Grassmann algebra and elementary number theory, Linear Multilinear Algebra 71(7) (2023) 1244–1264] in the PI theory context.\",\"PeriodicalId\":13756,\"journal\":{\"name\":\"International Journal of Algebra and Computation\",\"volume\":\" 85\",\"pages\":\"0\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Algebra and Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218196723500650\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Algebra and Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218196723500650","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
设[公式:见文]为特征不等于2的无限域上的无限维Grassmann代数[公式:见文]。本文的主要目的是描述[公式:见文]的分级多项式恒等式的[理想]和[公式:见文]的中心多项式的[公式:见文]空间及其[公式:见文]和[公式:见文]诱导的[公式:见文]分级。因此，我们推广了[A]的结果。brand， C. Fidelis和A. guimar，[公式:见文本]-格拉斯曼代数的完全支持度评分，数学学报，31 (2022):332-353;C. Fidelis, A. guimar es和P. Koshlukov，关于[公式:见文本]的注解-关于Grassmann代数和初等数论的评分，线性多线性代数，71(7)(2023)1244-1264]。
ℤ-Gradings on the Grassmann Algebra Over Infinite Fields: Graded Identities and Central Polynomials
Let [Formula: see text] be the infinite-dimensional Grassmann algebra over an infinite field [Formula: see text] of characteristic different from 2. The main purpose of this paper is to describe the [Formula: see text]-ideal of the graded polynomial identities and the [Formula: see text]-space of the central polynomials of [Formula: see text] equipped with its [Formula: see text] and [Formula: see text]-induced [Formula: see text]-gradings. Therefore, we generalize the results of [A. Brandão, C. Fidelis and A. Guimarães, [Formula: see text]-gradings of full support on the Grassmann algebra, J. Algebra 601 (2022) 332–353; C. Fidelis, A. Guimarães and P. Koshlukov, A note on [Formula: see text]-gradings on the Grassmann algebra and elementary number theory, Linear Multilinear Algebra 71(7) (2023) 1244–1264] in the PI theory context.
期刊介绍：
The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.
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