The residual character of varieties generated by strictly simple term minimal algebras (Q5950771)

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scientific article; zbMATH DE number 1682621
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The residual character of varieties generated by strictly simple term minimal algebras
scientific article; zbMATH DE number 1682621

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    The residual character of varieties generated by strictly simple term minimal algebras (English)
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    16 December 2001
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    An algebra is called strictly simple if it is finite, simple and has no nontrivial subalgebras. These algebras are important since every locally finite minimal variety contains a uniquely determined strictly simple algebra. In the paper the residual character of locally finite minimal varieties is investigated. It is shown that if \textbf{A} is a nonabelian strictly simple term minimal algebra, then the variety \texttt{V}(\textbf{A}) is either residually large or has \textbf{A} as its unique irreducible member, and it is possible to algorithmically decide the residual character of \texttt{V}(\textbf{A}) if \textbf{A} has finitely many fundamental operations.
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    residual smallness
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    subdirect irreducibility
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    strictly simple algebra
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    term minimal algebra
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    tame congruence theory
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    locally finite minimal varieties
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    residual character
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