无穷域上Grassmann代数上的n -分级:分级恒等式和中心多项式

IF 0.5 2区数学 Q3 MATHEMATICS International Journal of Algebra and Computation Pub Date : 2023-11-09 DOI:10.1142/s0218196723500650

Claudemir Fideles, Alan Guimaraes

{"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":null,"pages":null},"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\":null,\"pages\":null},\"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]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Algebra and Computation 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

6-12 weeks

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.