On the lattice of full eventually regular subsemigroups
نویسندگان
چکیده
We generalize to eventually regular (or ‘π-regular’) semigroups the study of the lattice of full regular subsemigroups of a regular semigroup, which has its most complete exposition in the case of inverse semigroups. By means of a judicious definition, it is shown that the full eventually regular subsemigroups of such a semigroup form a complete lattice LF , which projects onto the lattices of full regular subsemigroups of its regular principal factors. Our deepest results are obtained for those eventually regular semigroups in which the regular elements form a subsemigroup. In that case, LF also projects onto the lattice of full regular subsemigroups of that regular subsemigroup. In particular, we characterize such semigroups for which LF is distributive. A much more explicit description is obtained for the eventually regular semigroups in which the idempotents commute.
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