ASSOCIATIVE NIL-ALGEBRAS OVER FINITE FIELDS

DOI10.1142/S0218196713500471zbMath1298.16011arXiv1303.0898OpenAlexW2963455485MaRDI QIDQ5411788

Artem A. Lopatin, Ivan Pavlovic Shestakov

Publication date: 25 April 2014

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.0898

zbMATH Keywords

PI-algebrasnil-algebrasnilpotency classesrelatively free algebrasnilpotency degreesNagata-Higman theoremalgebras over finite fields

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Identities other than those of matrices over commutative rings (16R40)

Related Items (3)

Proper identities of finitely generated commutative alternative algebras ⋮ Estimates in Shirshov height theorem ⋮ A retrospect of the research in nonassociative algebras in IME-USP

Cites Work

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• An algorithm for computing graded algebras
• Rings of matrix invariants in positive characteristic
• On the nilpotency degree of the algebra with identity \(x^n=0\).
• Indecomposable Invariants of Quivers for Dimension (2,…,2) and Maximal Paths
• On minimal generating systems for matrixO(3)-invariants
• COMPUTING NILPOTENT QUOTIENTS OF ASSOCIATIVE ALGEBRAS AND ALGEBRAS SATISFYING A POLYNOMIAL IDENTITY
• The Algebra of Invariants of 3 × 3 Matrices Over a Field of Arbitrary Characteristic
• Relatively Free Algebras with the Identityx³ = 0^#

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