ℤ-gradings on the Grassmann algebra over infinite fields: Graded identities and central polynomials-Reference-Cited by-同舟云学术

ℤ-gradings on the Grassmann algebra over infinite fields: Graded identities and central polynomials

Published:2023-11-09 Issue:08 Volume:33 Page:1713-1735
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

Fideles Claudemir¹^ORCID,Guimarães Alan²^ORCID

Affiliation:

1. Department of Mathematics, Universidade Estadual de Campinas (UNICAMP), 13083-859 Campinas, SP, Brazil

2. Departamento de Matemática, Universidade Federal do Rio Grande do Norte, Natal, RN 59078-970, Brazil

Abstract

Let E be the infinite-dimensional Grassmann algebra over an infinite field F 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 E equipped with its [Formula: see text] and 3-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.

Funder

CNPq

FAPESP

FAPESQ-PB

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196723500650

Reference18 articles.

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5. Z2-graded identities of the Grassmann algebra in positive characteristic