Left absolutely flat generalized inverse semigroups

Bulman-Fleming, Sydney; McDowell, Kenneth

doi:10.1090/S0002-9939-1985-0792259-8

Left absolutely flat generalized inverse semigroups
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by Sydney Bulman-Fleming and Kenneth McDowell PDF

Proc. Amer. Math. Soc. 94 (1985), 553-561 Request permission

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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