Multiplicity type and subalgebra structure in infinitary universal algebras

Matthew Gould

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A generalization of the direct product of universal algebras

Abraham Goetz (1971)

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Universal Enveloping Algebras of Nonassociative Structures

Tvalavadze, Marina (2012)

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2010 Mathematics Subject Classification: Primary 17D15. Secondary 17D05, 17B35, 17A99. This is a survey paper to summarize the latest results on the universal enveloping algebras of Malcev algebras, triple systems and Leibniz n-ary algebras.

Universal algebras with all operations of bounded range

I. G. Rosenberg (1974)

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Not every equational class of infinitary algebras contains a simple algebra

Evelyn Nelson (1974)

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On normal Agassiz systems of algebras

Ewa Graczyńska, Andrzej Wroński (1978)

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The class of 2-dimensional neat reducts is not elementary

Tarek Sayed Ahmed (2002)

Fundamenta Mathematicae

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SC, CA, QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras and Halmos' quasipolyadic algebras with equality, respectively. Generalizing a result of Andréka and Németi on cylindric algebras, we show that for K ∈ SC,QA,CA,QEA and any β > 2 the class of 2-dimensional neat reducts of β-dimensional algebras in K is not closed under forming elementary subalgebras, hence is not elementary. Whether this result extends...