The Gelfand-Kirillov dimension of the universal algebras of \(M_{a,b}(E)\otimes E\) in positive characteristic.

DOI10.1007/s12215-011-0079-6zbMath1269.16015OpenAlexW2464787094MaRDI QIDQ693215

Fernanda G. de Paula, Sérgio M. Alves, Marcello Fidelis

Publication date: 7 December 2012

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/s12215-011-0079-6

zbMATH Keywords

Grassmann algebrasGelfand-Kirillov dimensiongraded identitiesverbally prime algebrasrelatively free algebrasT-prime algebrasT-prime T-ideals

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) 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)

Cites Work

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• Polynomial identities of algebras in positive characteristic.
• PI (non)equivalence and Gelfand-Kirillov dimension in positive characteristic.
• Tensor product theorems in positive characteristic.
• \(\mathbb{Z}_{k+l}\times\mathbb{Z}_2\)-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

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