PI (non)equivalence and Gelfand-Kirillov dimension in positive characteristic.

DOI10.1007/S12215-009-0011-5zbMath1192.16018OpenAlexW2050476110MaRDI QIDQ1032596

Sérgio Mota Alves

Publication date: 26 October 2009

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12215-009-0011-5

zbMATH Keywords

matrix algebrastensor productsT-idealsGrassmann algebrasGelfand-Kirillov dimensionpolynomial identitiesgraded identitiesverbally prime algebrasT-prime algebrasPI equivalent algebrasverbally prime PI algebras

Mathematics Subject Classification ID

Growth rate, Gelfand-Kirillov dimension (16P90) (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) Identities other than those of matrices over commutative rings (16R40)

Related Items (3)

Graded identities for algebras with elementary gradings over an infinite field ⋮ PI non-equivalence in positive characteristic. ⋮ The Gelfand-Kirillov dimension of the universal algebras of \(M_{a,b}(E)\otimes E\) in positive characteristic.

Cites Work

• Graded identities for T-prime algebras over fields of positive characteristic
• Polynomial identities of algebras in positive characteristic.
• The standard identity in characteristic \(p\): A conjecture of I. B. Volichenko
• Monomial algebras
• On the graded identities of \(M_{1,1}(E)\)
• Tensor products of matrix algebras over the Grassmann algebra
• Tensor product theorems in positive characteristic.
• Endomorphism rings of modules over PI-algebras
• \(\mathbb{Z}_{k+l}\times\mathbb{Z}_2\)-graded polynomial identities for \(M_{k,l}(E)\otimes E\).
• PI non-equivalence in positive characteristic.
• Grassmann algebras over finite fields
• Identities of associative algebras
• GRADED IDENTITIES AND PI EQUIVALENCE OF ALGEBRAS IN POSITIVE CHARACTERISTIC
• Generic verbally prime pi-algebras and their gk-dimensions
• Graded Polynomial Identities for Tensor Products by the Grassmann Algebra
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