Subalgebras of the squares of weakly diagonal majority algebras

Kalle Kaarli

doi:10.1556/sscmath.49.2012.4.1218

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 49: Issue 4

Subalgebras of the squares of weakly diagonal majority algebras

Author:

Kalle Kaarli

Kalle Kaarli University of Tartu Institute of Mathematics 50090 Tartu Estonia

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Pages:: 509–524

Online Publication Date:: 16 Nov 2012

Publication Date:: 01 Dec 2012

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.49.2012.4.1218

Keywords:: Primary 08C05; Secondary 08A30, 11A99, 20M30; Categorical equivalence; majority algebra; weakly diagonal algebra; ordered involutive monoid; lattice ordered semiring

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If A is a minimal algebra (that is, has no proper subalgebras) then the set S₂(A) of all subalgebras of A² has a natural structure of ordered involutive monoid. This paper gives a characterization of monoids S that appear in the role of this monoid if A is finite, weakly diagonal (every subalgebra of A² contains the graph of an automorphism of A) and has a majority term.

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Studia Scientiarum Mathematicarum Hungarica

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Studia Scientiarum Mathematicarum Hungarica
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