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Title of Journal: J Math Sci

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Abbravation: Journal of Mathematical Sciences

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Springer US

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DOI

10.1007/bf03258629

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1573-8795

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Simple and pseudosimple algebras with operators

Authors: V L Usoltsev
Publish Date: 2009/12/15
Volume: 164, Issue: 2, Pages: 281-
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Abstract

In this work algebras with operators ie algebras with an additional system of unary operations acting as endomorphisms with respect to the basic operations are considered We find necessary conditions for the simplicity and pseudosimplicity of an arbitrary universal algebra with a fixed operator and explore how several properties of congruences of this algebra depend on the structure of the unary reduct of a given algebra For algebras with one ternary operation defined in the standard way and satisfying the Mal’cev identities and one operator ie unars with Mal’cev operation necessary and sufficient conditions for their simplicity and pseudosimplicity are obtained

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