Finite Rings in Varieties with Definable Principal Congruences

DOI10.2307/2160258zbMath0810.16025OpenAlexW4237478058MaRDI QIDQ4306031

G. E. Simons

Publication date: 19 April 1995

Full work available at URL: https://doi.org/10.2307/2160258

zbMATH Keywords

finite ringvariety of ringsdefinable principal congruencesfirst-order formuladirect product of finite local rings

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Subalgebras, congruence relations (08A30) Noncommutative local and semilocal rings, perfect rings (16L30) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Identities other than those of matrices over commutative rings (16R40)

Related Items (1)

Definable principal congruences and solvability

Cites Work

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• Definable principal congruences in congruence distributive varieties
• A correction to Definable principal congruences in varieties of groups and rings
• Residually small varieties of K-algebras
• On classes of algebras with the definability of congruences
• Representations of finite rings
• The number of subdirectly irreducible algebras in a variety
• Para primal varieties: A study of finite axiomatizability and definable principal congruences in locally finite varieties
• Definable principal congruences in varieties of groups and rings
• Definable Principal Congruences and R-Stable Identities
• The Structure of Rings in Some Varieties with Definable Principal Congruences
• Varieties of Rings with Definable Principal Congruences
• Separable Algebras Over Commutative Rings

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