zbMATH — the first resource for mathematics

Proper weakly left ample semigroups. (English) Zbl 0948.20036
Much of the structure theory of inverse semigroups is based on constructing arbitrary inverse semigroups from groups and semilattices. Celebratedly, $$E$$-unitary (or proper) inverse semigroups are known to be $$P$$-semigroups (McAlister), or inverse subsemigroups of semidirect products of a semilattice by a group (O’Carroll) or $$C_u$$-semigroups built over an inverse category acted upon by a group (Margolis and Pin). On the other hand, every inverse semigroup is known to have an $$E$$-unitary inverse cover (McAlister).
The aim of this paper is to develop a similar theory for proper weakly left ample semigroups, a class with properties echoing those of inverse semigroups. We show how the structure of semigroups in this class is based on constructing semigroups from unipotent monoids and semilattices. The results corresponding to those of McAlister, O’Carroll and Margolis and Pin are obtained.

MSC:
 20M10 General structure theory for semigroups
Full Text:
References:
 [1] DOI: 10.1017/S0017089500031840 · Zbl 0871.20054 [2] DOI: 10.1093/qmath/28.3.285 · Zbl 0377.20051 [3] DOI: 10.1112/blms/22.4.353 · Zbl 0724.20040 [4] DOI: 10.1016/0022-4049(92)90066-O · Zbl 0774.20047 [5] DOI: 10.1017/S0017089500009873 · Zbl 0802.20051 [6] Fountain J., Portugaliae Math. 5 pp 1– (1994) [7] DOI: 10.1006/jabr.1999.7871 · Zbl 0940.20064 [8] DOI: 10.1080/00927879908826450 · Zbl 0926.20039 [9] DOI: 10.1016/0021-8693(87)90046-9 · Zbl 0625.20043 [10] McAlister D. B., Trans. Amer. Math. Soc. 192 pp 227– (1974) [11] DOI: 10.1090/S0002-9947-74-99950-4 [12] DOI: 10.1017/S2040618500034286 · Zbl 0113.02403 [13] DOI: 10.1016/0021-8693(76)90023-5 · Zbl 0343.20037 [14] DOI: 10.1016/0022-4049(87)90108-3 · Zbl 0627.20031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.