Regular congruences on Croisot-Teissier and Baer-Levi semigroups
Bruce W. Mielke · Journal of the Mathematical Society of Japan · 1972
Clifford and Preston have defined a class of Croisot-Teissier semigroups of type $(p, q)$ which are simple with a minimal right ideal when $p=q([1]$ $8.2)$ .In this paper, we define a modified class of Croisot-Teissier semigroups (1.3) which are simple with a minimal right ideal for all $q\leqq p$ (1.9).The generalized Baer-Levi semigroups ([1] 8.1) are shown to be right simple generalized Croisot-Teissier semigroups under the new definition (1.5).In the concluding sections, we investigate group and band congruences on these semigroups.We find a set, $E$ , which is contained in the kernel of