Fuzzy congruences on \(T^*\)-pure semigroups. (English) Zbl 0871.20052
Let \(\alpha\) be a fuzzy congruence relation on a semigroup \(S\). Then \(\alpha\) is a group [a semilattice] fuzzy congruence on \(S\) if \(S/\alpha\) is a group [a semilattice]. We give some properties of a group [a semilattice] fuzzy congruence on a \(T^*\)-pure semigroup.
MSC:
| 20M10 | General structure theory for semigroups |
| 08A30 | Subalgebras, congruence relations |
| 20M15 | Mappings of semigroups |
| 20N25 | Fuzzy groups |
References:
| [1] | Kuroki, N., \(T^∗- pure\) Archimedean semigroups, Comment. Math. Univ. St. Pauli, 31, 115-128 (1982) · Zbl 0507.20032 |
| [2] | Kuroki, N., On a weakly idempotent semigroup in which the idempotents are central, Joetsu, J. Math. Educ., 2, 19-28 (1987) |
| [3] | N. Kuroki, Fuzzy congruences on inverse semigroups (submitted).; N. Kuroki, Fuzzy congruences on inverse semigroups (submitted). · Zbl 0916.20048 |
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