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On normal semigroups. (English) Zbl 0358.20074
A subsemigroup $$A$$ of a semigroup $$S$$ is called a bi-ideal of $$S$$ if $$ASA \subseteq A$$. The set of all bi-ideals of a semigroup $$S$$ is also a semigroup under the multiplication of subsets, which we denote by $$B(S)$$. A semigroup $$S$$ is called normal if $$xS=Sx$$ for all $$x \in S$$, and is called viable if $$ab = ba$$ whenever $$ab$$ and $$ba$$ are idempotents. The author gives characterizations of semigroups that are semilattices of groups: For a semigroup $$S$$ the following conditions are equivalent:
(1) $$S$$ is a semilattice of groups.
(2) $$B(S)$$ is a semilattice of groups.
(3) $$B(S)$$ is regular and normal.
(4) $$B(S)$$ is regular and viable.
Reviewer: Nuboaki Kuroki
Show Scanned Page ##### MSC:
 20M10 General structure theory for semigroups
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##### References:
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