GRADED IDENTITIES AND PI EQUIVALENCE OF ALGEBRAS IN POSITIVE CHARACTERISTIC

DOI10.1081/AGB-200053801zbMath1077.16024OpenAlexW2032717924MaRDI QIDQ4681020

Plamen Koshlukov, Marcello Fidelis, Sérgio S. de Azevedo

Publication date: 14 June 2005

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/agb-200053801

zbMATH Keywords

matrix algebrasGrassmann algebrasgraded polynomial identitiesalgebras with polynomial identityT-prime T-idealsbases of graded identities

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Endomorphism rings; matrix rings (16S50) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Graded rings and modules (associative rings and algebras) (16W50) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Exterior algebra, Grassmann algebras (15A75) Semiprime p.i. rings, rings embeddable in matrices over commutative rings (16R20)

Related Items (14)

Graded identities for algebras with elementary gradings over an infinite field ⋮ Polynomial identities of algebras in positive characteristic. ⋮ Central polynomials for \(\mathbb{Z}_2\)-graded algebras and for algebras with involution. ⋮ PI non-equivalence in positive characteristic. ⋮ Unnamed Item ⋮ \(\mathbb{Z}\)-graded identities of the Virasoro algebra ⋮ The Gelfand-Kirillov dimension of the universal algebras of \(M_{a,b}(E)\otimes E\) in positive characteristic. ⋮ Polynomial identities for graded tensor products of algebras. ⋮ Graded identities of several tensor products of the Grassmann algebra ⋮ PI (non)equivalence and Gelfand-Kirillov dimension in positive characteristic. ⋮ Identities of PI-Algebras Graded by a Finite Abelian Group ⋮ The graded Gelfand--Kirillov dimension of verbally prime algebras ⋮ Graded identities for Kac-Moody and Heisenberg algebras with the Cartan grading ⋮ Graded identities for tensor products of matrix (super)algebras over the Grassmann algebra

Cites Work

• Unnamed Item
• Identities of the tensor square of a Grassmann algebra
• A minimal basis of identities for a second-order matrix algebra over a field of characteristic 0
• Central polynomials in the matrix algebra of order two.
• On the graded identities of \(M_{1,1}(E)\)
• Tensor products of matrix algebras over the Grassmann algebra
• Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero
• Tensor product theorems in positive characteristic.
• Grassmann algebras over finite fields
• $\mathbf {Z}_n$-graded polynomial identities of the full matrix algebra of order $n$
• Generic verbally prime pi-algebras and their gk-dimensions
• GRADED IDENTITIES FOR THE MATRIX ALGEBRA OF ORDER OVER AN INFINITE FIELD
• Graded Polynomial Identities for Tensor Products by the Grassmann Algebra

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