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Semilattices of subdimonoids. (English) Zbl 1232.08002

Summary: We present some congruence on the dimonoid with an idempotent operation and use it to obtain semilattice decompositions of an idempotent dimonoid. Also we give necessary and sufficient conditions under which an arbitrary dimonoid is a semilattice of archimedean subdimonoids.

MSC:

08A05 Structure theory of algebraic structures
08A30 Subalgebras, congruence relations
20M99 Semigroups
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