On a class of Dubreil-Jacotin regular semigroups and a construction of Yamada
- 1 January 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 77 (1-2) , 145-150
- https://doi.org/10.1017/s0308210500018102
Abstract
In the publication [2] we obtained some structure theorems for certain Dubreil-Jacotin regular semigroups. A crucial observation in the course of investigating these types of ordered regular semigroups was that the (ordered) band of idempotents was normal. This is characteristic of a class of semigroups studied by Yamada [5] and called generalised inverse semigroups. Here we specialise a construction of Yamada to obtain a structure theorem that complements those in [2], The important feature of the present approach is the part played by the greatest elements that exist in each of the components in the semilattice decompositions involved.Keywords
This publication has 2 references indexed in Scilit:
- 21.—The Structure of certain Ordered Regular SemigroupsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1976
- Regular semi-groups whose idempotents satisfy permutation identitiesPacific Journal of Mathematics, 1967