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2011•Demonstratio MathematicaOpen access

Some semilattice decompositions of dimonoids

Anatolii V. Zhuchok

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Abstract

Abstract We show that the system of axioms of a dimonoid is independent and prove that every dimonoid with a commutative operation is a semilattice of archimedean subdimonoids, every dimonoid with a commutative periodic semigroup is a semilattice of unipotent subdimonoids, every dimonoid with a commutative operation is a semilattice ofa-connected subdimonoids and every idempotent dimonoid is a semilattice of rectangular subdimonoids.

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Abstract We show that the system of axioms of a dimonoid is independent and prove that every dimonoid with a commutative operation is a semilattice of archimedean subdimonoids, every dimonoid with a commutative periodic semigroup is a semilattice of unipotent subdimonoids, every dimonoid with a commutative operation is a semilattice ofa-connected subdimonoids and every idempotent dimonoid is a semilattice of rectangular subdimonoids.

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Available abstract

Abstract We show that the system of axioms of a dimonoid is independent and prove that every dimonoid with a commutative operation is a semilattice of archimedean subdimonoids, every dimonoid with a commutative periodic semigroup is a semilattice of unipotent subdimonoids, every dimonoid with a commutative operation is a semilattice ofa-connected subdimonoids and every idempotent dimonoid is a semilattice of rectangular subdimonoids.

Key concepts: Semilattice, Mathematics, Pure mathematics, Algebra over a field, Semigroup

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