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Semilattice pseudo-complements on semigroups. (English) Zbl 1069.20055

The notion of a pseudo-complement semigroup \(S\) (relative to a distinguished subsemilattice \(L\) of \(S\)) is extended to a broad class of semigroups (definitions are too technical to record here). The relationship between these semigroups and those with closure and interior operations is examined and the concepts are considered in a ring setting as well.
Classes of congruences on these so called SP-semigroups are described. The class of SP-semilattices coincides with a natural class of ordered structures related to topological spaces.

MSC:

20M10 General structure theory for semigroups
06A12 Semilattices
16W99 Associative rings and algebras with additional structure
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References:

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