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Left absolutely flat generalized inverse semigroups

Authors: Sydney Bulman-Fleming and Kenneth McDowell
Journal: Proc. Amer. Math. Soc. 94 (1985), 553-561
MSC: Primary 20M10; Secondary 20M50
MathSciNet review: 792259
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Abstract: A semigroup $ S$ is called (left, right) absolutely flat if all of its (left, right) $ S$-sets are flat. $ S$ is a (left, right) generalized inverse semigroup if $ S$ is regular and its set of idempotents $ E(S)$ is a (left, right) normal band (i.e. a strong semilattice of (left zero, right zero) rectangular bands). In this paper it is proved that a generalized inverse semigroup $ S$ is left absolutely flat if and only if $ S$ is a right generalized inverse semigroup and the (nonidentity) structure maps of $ E(S)$ are constant. In particular all inverse semigroups are left (and right) absolutely flat (see [1]). Other consequences are derived.

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Keywords: Generalized inverse semigroup, absolutely flat semigroup, normal band
Article copyright: © Copyright 1985 American Mathematical Society

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