{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T17:19:33Z","timestamp":1671729573883},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2016,12]]},"abstract":"<jats:p> Let [Formula: see text] be a field of characteristic 0 and let [Formula: see text]. The algebra [Formula: see text] admits a natural grading [Formula: see text] by the cyclic group [Formula: see text] of order 2. In this paper, we describe the [Formula: see text]-graded A-identities for [Formula: see text]. Recall that an A-identity for an algebra is a multilinear polynomial identity for that algebra which is a linear combination of the monomials [Formula: see text] where [Formula: see text] runs over all even permutations of [Formula: see text] that is [Formula: see text], the [Formula: see text]th alternating group. We first introduce the notion of an A-identity in the case of graded polynomials, then we describe the graded A-identities for [Formula: see text], and finally we compute the corresponding graded A-codimensions. <\/jats:p>","DOI":"10.1142\/s0218196716500715","type":"journal-article","created":{"date-parts":[[2016,11,25]],"date-time":"2016-11-25T04:26:06Z","timestamp":1480047966000},"page":"1617-1631","source":"Crossref","is-referenced-by-count":2,"title":["Graded A-identities for the matrix algebra of order two"],"prefix":"10.1142","volume":"26","author":[{"suffix":"Jr.","given":"Antonio Pereira","family":"Brand\u00e3o","sequence":"first","affiliation":[{"name":"Department of Mathematics, Federal University of Campina Grande, 58429-970 Campina Grande, PB, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dimas Jos\u00e9","family":"Gon\u00e7alves","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Federal University of S\u00e3o Carlos, 13565-905 S\u00e3o Carlos, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Plamen","family":"Koshlukov","sequence":"additional","affiliation":[{"name":"Department of Mathematics, IMECC, UNICAMP, S\u00e9rgio Buarque de Holanda 651, 13083-859 Campinas, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,12,20]]},"reference":[{"key":"S0218196716500715BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02785422"},{"key":"S0218196716500715BIB002","doi-asserted-by":"publisher","DOI":"10.1201\/9780203911549.ch4"},{"key":"S0218196716500715BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s00605-008-0046-2"},{"key":"S0218196716500715BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02808074"},{"key":"S0218196716500715BIB005","volume-title":"Free algebras and PI-algebras: Graduate Course in Algebra","author":"Drensky V.","year":"1999"},{"key":"S0218196716500715BIB006","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/122"},{"key":"S0218196716500715BIB007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-08-09281-2"},{"key":"S0218196716500715BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-011-0146-x"},{"key":"S0218196716500715BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00013-016-0882-6"},{"key":"S0218196716500715BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02773073"},{"key":"S0218196716500715BIB011","doi-asserted-by":"publisher","DOI":"10.1070\/IM1985v025n02ABEH001285"},{"key":"S0218196716500715BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/BF01978692"},{"key":"S0218196716500715BIB013","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2000.8738"},{"key":"S0218196716500715BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S021819670800469X"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196716500715","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:04:09Z","timestamp":1565118249000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196716500715"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12]]},"references-count":14,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2016,12,20]]},"published-print":{"date-parts":[[2016,12]]}},"alternative-id":["10.1142\/S0218196716500715"],"URL":"https:\/\/doi.org\/10.1142\/s0218196716500715","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,12]]}}}