The word problem in varieties of semigroups, rings, and Lie algebras

DOI10.1007/BF00970009zbMath0653.20060OpenAlexW2057457167MaRDI QIDQ1107640

O. G. Kharlampovich, I. L. Mel'nichuk, Mark V. Sapir

Publication date: 1986

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00970009

zbMATH Keywords

identitiesfinitely presented semigroupsvariety of semigroupsstandard identityminimal varietybasis of identitiesundecidable word problem

Mathematics Subject Classification ID

Lattices of varieties (08B15) Varieties and pseudovarieties of semigroups (20M07) Free semigroups, generators and relations, word problems (20M05) Infinite-dimensional Lie (super)algebras (17B65) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Quasivarieties and varieties of groups (20E10) Word problems (aspects of algebraic structures) (08A50) Rings with polynomial identity (16Rxx)

Cites Work

• Finite basis theorem for systems of semigroup identities
• The equality problem and free products of Lie algebras and of associative algebras
• Subalgebras of finitely presented solvable Lie algebras
• Bases for equational theories of semi-groups
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