ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXV, 1 (2006)
p. 1 - 19

Onesided inverses for semigroups
M. Petrich

Abstract. In any semigroup S, we say that elements a and b are left inverses of each other if a = aba, b=bab and a L b, in which case we write a g b. Right inverses are defined dually with the notation d. Set t = bg . We study the classes of semigroups in which t has some of the usual properties of a relation. We also consider properties of (maximal) completely simple subsemigroups of S.
In terms of the above concepts, we characterize E-solid, central, (almost) L -unipotent and locally (almost) L -unipotent semigroups in many ways. We define these notions for arbitrary semigroups by extending their definitions from regular semigroups.

Keywords: Semigroup, inverse, onesided inverse, e-solid, E-solid, idempotent square, central, completely regular, almost q-idempotent, locally almost q-idempotent, regular.

AMS Subject classification: Primary 20M99; Secondary 20M17.

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Acta Mathematica Universitatis Comenianae
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