{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T23:11:00Z","timestamp":1649200260577},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2016,9]]},"abstract":"<jats:p> Let [Formula: see text] be a finite abelian group. As a consequence of the results of Di Vincenzo and Nardozza, we have that the generators of the [Formula: see text]-ideal of [Formula: see text]-graded identities of a [Formula: see text]-graded algebra in characteristic 0 and the generators of the [Formula: see text]-ideal of [Formula: see text]-graded identities of its tensor product by the infinite-dimensional Grassmann algebra [Formula: see text] endowed with the canonical grading have pairly the same degree. In this paper, we deal with [Formula: see text]-graded identities of [Formula: see text] over an infinite field of characteristic [Formula: see text], where [Formula: see text] is [Formula: see text] endowed with a specific [Formula: see text]-grading. We find identities of degree [Formula: see text] and [Formula: see text] while the maximal degree of a generator of the [Formula: see text]-graded identities of [Formula: see text] is [Formula: see text] if [Formula: see text]. Moreover, we find a basis of the [Formula: see text]-graded identities of [Formula: see text] and also a basis of multihomogeneous polynomials for the relatively free algebra. Finally, we compute the [Formula: see text]-graded Gelfand\u2013Kirillov (GK) dimension of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196716500478","type":"journal-article","created":{"date-parts":[[2016,6,17]],"date-time":"2016-06-17T05:55:46Z","timestamp":1466142946000},"page":"1125-1140","source":"Crossref","is-referenced-by-count":1,"title":["A note on graded polynomial identities for tensor products by the Grassmann algebra in positive characteristic"],"prefix":"10.1142","volume":"26","author":[{"given":"Lucio","family":"Centrone","sequence":"first","affiliation":[{"name":"Universidade Estadual de Campinas, Rua Sergio Buarque de Holanda 651, Campinas (SP), 13083-859, Brazil"}]},{"given":"Viviane Ribeiro Tomaz","family":"da Silva","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto de Ci\u00eancias Exatas, Universidade Federal de Minas Gerais, Belo Horizonte, 31270-901, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2016,8,31]]},"reference":[{"key":"S0218196716500478BIB001","doi-asserted-by":"publisher","DOI":"10.1070\/SM2000v191n03ABEH000460"},{"key":"S0218196716500478BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2011.06.008"},{"issue":"1","key":"S0218196716500478BIB003","first-page":"43","volume":"38","author":"Centrone L.","year":"2012","journal-title":"Serdica Math. 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