On the structure of two generalizations of the full inverse symmetric semigroup
نویسندگان
چکیده
We introduce two generalizations of the full inverse symmetric semigroup ISX — the inverse semigroups PIPX and P̃IPX . Both of these semigroups have the same set of elements and contain ISX . The binary operations on PIPX and P̃IPX are two natural generalizations of the multiplication of partial permutations and each of the considered operations coincides with this multiplication when restricted to ISX . For each of the introduced semigroups there are two realizations: via partitions and via difunctional binary relations. Using the very illustrative realization via partitions, we study the algebraic properties of the semigroups PIPX and P̃IPX , in particular, establish the structure of ideals, Green’s relations, maximal subsemigroups, maximal inverse subsemigroups, maximal nilpotent subsemigroups, congruences, completely isolated and isolated subsemigroups, automorphism groups and describe all faithful transitive effective representations by partial permutations. 2000 Mathematics Subject Classification 20M10, 20M20.
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