On ℤ2-graded identities of the super tensor product of UT 2(F) by the Grassmann algebra

On -graded identities of the generalized Grassmann envelope of the upper triangular matrices

“…It is worth noting that Corollary 14, Proposition 15 and Theorem 17 together constitute an important generalization of Theorems 3.5 and 3.6 of [6]. Furthermore, Proposition 15 and Theorem 17 together generalize Theorems 8, 9 and 12 of [24].…”

“…By Lemma 3 of [24] and Proposition 10, the space Γ t,1 is spanned, modulo I, by polynomials ũ = ṽ[z 1 , y l 1 , . .…”

“…Hence these superalgebras satisfy the same Z 2 -graded identities. A first step in the study of their Z 2 -graded polynomial identities was concluded by da Silva (see [24]) with the description of the T 2 -ideal Id gr (UT 1,1 (E)). Although the description of the graded identities of UT k,l (E) for some particular cases is a consequence of [4,2], giving a description of Id gr (UT k,l (E))…”