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The greatest idempotent-separating congruence and group congruences on a weakly inverse semigroup. (Chinese. English summary) Zbl 0996.20047

Summary: The greatest idempotent-separating congruence and the minimum group congruence on a weakly inverse semigroup \(S\) are characterized. It is proved that the lattice of group congruences on \(S\) is a complete lattice isomorphic to the lattice of group congruences on \(I(S)\), the inverse subsemigroup of principal elements of \(S\). Moreover, the lattice of group congruences of \(S\) is also a lattice homomorphic image of the lattice of all congruences of \(S\).

MSC:

20M18 Inverse semigroups
08A30 Subalgebras, congruence relations
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