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Regular semigroups which are subdirect products of a band and a semilattice of groups. (English) Zbl 0257.20055

Summary: The paper contains various results on the semigroups defined in the title. These semigroups are precisely orthodox bands of groups. A regular semigroup is a subdirect product of a band (= an idempotent semigroup) and a group if and only if it is a band of groups and its subset of idempotents is unitary. Regular semigroups which are subdirect products of a rectangular band and a semilattice of groups are characterized. Each of these and other classes of regular semigroups are presented as certain standard subdirect products (usually spined products) of bands and semilattices of groups, the theorems of equivalence for such presentations are established.
Reviewer: Boris M. Schein

MSC:

20M17 Regular semigroups
20M19 Orthodox semigroups
06A12 Semilattices
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References:

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