Yu, Bingjun; Yu, Shiwei; Liao, Qunying The greatest idempotent-separating congruence and group congruences on a weakly inverse semigroup. (Chinese. English summary) Zbl 0996.20047 J. Sichuan Norm. Univ., Nat. Sci. 24, No. 3, 219-223 (2001). 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 \(S\). Cited in 1 ReviewCited in 1 Document MSC: 20M18 Inverse semigroups 08A30 Subalgebras, congruence relations Keywords:idempotent-separating congruences; weakly inverse semigroups; lattices of group congruences; complete lattices; principal elements; lattices of congruences PDFBibTeX XMLCite \textit{B. Yu} et al., J. Sichuan Norm. Univ., Nat. Sci. 24, No. 3, 219--223 (2001; Zbl 0996.20047)