A Note on Semilattice Decompositions of Completely Π-regular Semigroups
نویسندگان
چکیده
We study completely π-regular semigroups admitting a decomposition into a semilattice of σn-simple semigroups, and describe them in terms of properties of their idempotents. In the general case, semigroups admitting a decomposition into a semilattice of σn-simple semigroups were characterized by M. Ćirić and S. Bogdanović in [3] (see Theorem 1 below), in terms of paths of length n in the graph corresponding to the relation −→, and in terms of principal filters and n-radicals. Here we prove that in the completely π-regular case, it suffices to consider only those paths of length n starting and/or ending with and idempotent, as well as principal filters and n-radicals generated by idempotents. AMS Mathematics Subject Classification (2000): 20M10
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