One-sided congruences on inverse semigroups

John Meakin
1975 Transactions of the American Mathematical Society  
By the kernel of a one-sided (left or right) congruence p on an inverse semigroup S, we mean the set of p-classes which contain idempotents of S. We provide a set of independent axioms characterizing the kernel of a one-sided congruence on an inverse semigroup and show how to reconstruct the one-sided congruence from its kernel. Next we show how to characterize those partitions of the idempotents of an inverse semigroup S which are induced by a one-sided congruence on S and provide a
more » ... rovide a characterization of the maximum and minimum one-sided congruences on S inducing a given such partition. The final two sections are devoted to a study of indempotent-separating one-sided congruences and a characterization of all inverse semigroups with only trivial full inverse subsemigroups. A Green-Lagrange-type theorem for finite inverse semigroups is discussed in the fourth section.
doi:10.1090/s0002-9947-1975-0369580-9 fatcat:7gzuwsotc5hejeqeshhlny3qiu