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 Algebra Logika: Year: Volume: Issue: Page: Find

 Algebra Logika, 2003, Volume 42, Number 1, Pages 107–122 (Mi al20)

Iterative Algebras without Projections

K. L. Safin, E. V. Sukhanov

Ural State University

Abstract: We deal with iterative algebras of functions of $k$-valued logic lacking projections, which we call algebras without projections. It is shown that a partially ordered set of algebras of functions of $m$-valued logic, for $m>k$, without projections contains an interval isomorphic to the lattice of all iterative algebras of functions of $k$-valued logic. It is found out that every algebra without projections is contained in some maximal algebra without projections, which is the stabilizer of a semigroup of non-surjective transformations of the basic set. It is proved that the stabilizer of a semigroup of all monotone non-surjective transformations of a linearly ordered 3-element set is not a maximal algebra without projections, but the stabilizer of a semigroup of all transformations preserving an arbitrary non one-element subset of the basic set is.

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English version:
Algebra and Logic, 2003, 42:1, 61–69

Bibliographic databases:

UDC: 512.565.5
Revised: 10.09.2002

Citation: K. L. Safin, E. V. Sukhanov, “Iterative Algebras without Projections”, Algebra Logika, 42:1 (2003), 107–122; Algebra and Logic, 42:1 (2003), 61–69

Citation in format AMSBIB
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\paper Iterative Algebras without Projections
\jour Algebra Logika
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1988026}
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\jour Algebra and Logic
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\vol 42
\issue 1
\pages 61--69
\crossref{https://doi.org/10.1023/A:1022632925246}
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