Turkish Journal

of

Mathematics

math@tubitak.gov.tr

# Turkish Journal of Mathematics

On Certain Varieties of Semigroups

Andreas TIEFENBACH
Middle East Technical University,
Department of Mathematics,
06531, Ankara-TURKEY

Abstract: In this paper we generalize the class of completely regular semigroups (unions of groups) to the class of local monoids, that is the class of all semigroups where the local subsemigroups $$aSa$$ are local submonoids. The sublattice of this variety $$(\mathbf{L}(\caL(\cam))$$ covers another lattice isomorphic to the lattice of all bands $$([x2 = x]).$$ Every bundvariety $$\cau$$ has as image the variety $$F - \cau,$$ which is the class of all semigroups, where $$F$$ is a $$\cau$$-congruence $$(a F b \Leftrightarrow aSa = bSb).$$ It is shown how one can find the laws for $$F - \cau$$ for a given bandvariety $$\cau$$. The laws for $$F - \cab$$ are given and it is shown that $$F - \car\cab - \caL(\cag) \caL(\cav) := \{S : aSa \in \cav \forall a \in S\}).$$

Turk. J. Math., 22, (1998), 145-152.
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Other articles published in the same issue: Turk. J. Math.,vol.22,iss.2.