Di Vincenzo, Onofrio Mario; Nardozza, Vincenzo \(\mathbb{Z}_{k+l}\times\mathbb{Z}_2\)-graded polynomial identities for \(M_{k,l}(E)\otimes E\). (English) Zbl 1147.16302 Rend. Semin. Mat. Univ. Padova 108, 27-39 (2002). Summary: Let \(K\) be a field of characteristic zero, and \(E\) be the Grassmann algebra over an infinite-dimensional \(K\)-vector space. We endow \(M_{k,l}(E)\otimes E\) with a \(\mathbb{Z}_{k+l}\times\mathbb{Z}_2\)-grading, and determine a generating set for the ideal of its graded polynomial identities. As a consequence, we prove that \(M_{k,l}(E)\times E\) and \(M_{k+l}(E)\) are PI-equivalent with respect to this grading. In particular, this leads to their ordinary PI-equivalence, a classical result obtained by Kemer. Cited in 9 Documents MSC: 16R50 Other kinds of identities (generalized polynomial, rational, involution) 16R10 \(T\)-ideals, identities, varieties of associative rings and algebras 15A75 Exterior algebra, Grassmann algebras Keywords:Grassmann algebras; generating sets; ideals of graded polynomial identities; PI-equivalences PDFBibTeX XMLCite \textit{O. M. Di Vincenzo} and \textit{V. Nardozza}, Rend. Semin. Mat. Univ. Padova 108, 27--39 (2002; Zbl 1147.16302) Full Text: EuDML References: [1] A. BERELE, Supertraces and matrices over Grassmann algebras, Advances in Math., 108 (1) (1994), pp. 77-90. Zbl0819.16023 MR1293582 · Zbl 0819.16023 [2] O. M. DI VINCENZO - V. NARDOZZA, Graded polynomial identities for tensor products by the Grassmann Algebra, Comm. Algebra (2002) (in press). Zbl1039.16023 · Zbl 1039.16023 [3] A. R. KEMER, Varieties and Z2-graded algebras, Math. USSR Izv., 25 (1985), pp. 359-374. Zbl0586.16010 MR764308 · Zbl 0586.16010 [4] A. R. KEMER, Ideals of identities of associative algebras, AMS Trans. of Math. Monographs, 87 (1991). Zbl0732.16001 MR1108620 · Zbl 0732.16001 [5] A. REGEV, Tensor product of matrix algebras over the Grassmann algebra, J. Algebra, 133 (1990), pp. 351-369. Zbl0639.16010 MR1067423 · Zbl 0639.16010 [6] S. Y. VASILOVSKY, Zn-graded polynomial identities of the full matrix algebra of order n, Proc. Amer. Math. Soc., 127 (12) (1999), pp. 3517-3524. Zbl0935.16012 MR1616581 · Zbl 0935.16012 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.