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J. Algebra Comput."],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:p> 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.\u00a0Brand\u00e3o, C.\u00a0Fidelis and A.\u00a0Guimar\u00e3es, [Formula: see text]-gradings of full support on the Grassmann algebra, J.\u00a0Algebra\u00a0601 (2022) 332\u2013353; C.\u00a0Fidelis, A.\u00a0Guimar\u00e3es and\u00a0P. Koshlukov, A\u00a0note on [Formula: see text]-gradings on the Grassmann algebra and elementary number theory, Linear Multilinear Algebra\u00a071(7) (2023) 1244\u20131264] in the PI theory context. <\/jats:p>","DOI":"10.1142\/s0218196723500650","type":"journal-article","created":{"date-parts":[[2023,9,30]],"date-time":"2023-09-30T01:53:20Z","timestamp":1696038800000},"page":"1713-1735","source":"Crossref","is-referenced-by-count":0,"title":["\u2124-gradings on the Grassmann algebra over infinite fields: Graded identities and central polynomials"],"prefix":"10.1142","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5107-5342","authenticated-orcid":false,"given":"Claudemir","family":"Fideles","sequence":"first","affiliation":[{"name":"Department of Mathematics, Universidade Estadual de Campinas (UNICAMP), 13083-859 Campinas, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4492-8818","authenticated-orcid":false,"given":"Alan","family":"Guimar\u00e3es","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade Federal do Rio Grande do Norte, Natal, RN 59078-970, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2023,11,9]]},"reference":[{"key":"S0218196723500650BIB001","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-100105997"},{"key":"S0218196723500650BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2017.07.005"},{"key":"S0218196723500650BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-010-0074-1"},{"key":"S0218196723500650BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2022.03.014"},{"key":"S0218196723500650BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2011.06.008"},{"key":"S0218196723500650BIB006","doi-asserted-by":"publisher","DOI":"10.5817\/AM2016-3-141"},{"key":"S0218196723500650BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2020.05.019"},{"key":"S0218196723500650BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2009.02.005"},{"volume-title":"Free Algebras and PI-Algebras. 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