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A class of globally determined Clifford semigroups. (English) Zbl 1313.20052

Summary: An element of a semilattice is called prime (in terms of lattices, “meet irreducible”) if it cannot be expressed as a product of two elements distinct from itself. In this paper, we show that the class of Clifford semigroups whose semilattices are generated by their prime elements are globally determined. This extends the result given by M. Gould and J. A. Iskra [Semigroup Forum 28, 1-11 (1984; Zbl 0528.20046)].

MSC:

20M17 Regular semigroups
06A12 Semilattices
20M10 General structure theory for semigroups

Citations:

Zbl 0528.20046
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