Affine representability and decision procedures for commutativity theorems for rings and algebras

DOI10.1007/s11856-022-2309-3OpenAlexW3126938352WikidataQ113899775 ScholiaQ113899775MaRDI QIDQ2164418

Jason P. Bell, Peter V. Danchev

Publication date: 15 August 2022

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.00357

zbMATH Keywords

commutativity theoremsrepresentabilitypolynomial identityPI-algebraSpecht problem

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

Cites Work

• Kemer's theorem for affine PI algebras over a field of characteristic zero.
• Power maps in rings
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• Multiplicative commutators in division rings
• Matrix type of some algebras over a field of characteristic \(p\)
• Rings with all modules residually finite
• Existence of identities in \(A \otimes B\)
• Gesetze in Ringen. I
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• A Condition for the Commutativity of Rings
• The local finite basis property and local representability of varieties of associative rings
• Standard Gröbner-Shirshov Bases of Free Algebras Over Rings, I
• Identities of associative algebras
• Combinatorial Nullstellensatz
• Counterexamples to the Specht problem
• IDENTITIES OF FINITELY GENERATED ALGEBRAS OVER AN INFINITE FIELD
• MULTILINEAR IDENTITIES OF THE ALGEBRAS OVER A FIELD OF CHARACTERISTIC P
• A note on a theorem of Jacobson related to periodic rings
• Gröbner–Shirshov bases and their calculation
• Specht’s problem for associative affine algebras over commutative Noetherian rings
• Residually Finite Rings
• A Generalization of a Theorem of Jacobson III
• Algorithms for construction of standard Gröbner-Shirshov bases of ideals of free algebras over commutative rings
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