Lattice isomorphisms of bisimple monogenic orthodox semigroups
Abstract
Using the classification and description of the structure of bisimple monogenic orthodox semigroups obtained in key10, we prove that every bisimple orthodox semigroup generated by a pair of mutually inverse elements of infinite order is strongly determined by the lattice of its subsemigroups in the class of all semigroups. This theorem substantially extends an earlier result of key25 stating that the bicyclic semigroup is strongly lattice determined.
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