Geodesic
Associate subgroups of orthodox semigroups
Glasgow mathematical journal, Tome 36 (1994) no. 2, pp. 163-171

Voir la notice de l'article provenant de la source Cambridge University Press

A unit regular semigroup [1, 4] is a regular monoid S such that H1 ∩ A(x) ≠ Ø for every xɛS, where H1, is the group of units and A(x) = {y ɛ S; xyx = x} is the set of associates (or pre-inverses) of x. A uniquely unit regular semigroupis a regular monoid 5 such that |H1 ∩ A(x)| = 1. Here we shall consider a more general situation. Specifically, we consider a regular semigroup S and a subsemigroup T with the property that |T ∩ A(x) = 1 for every x ɛ S. We show that T is necessarily a maximal subgroup Hα for some idempotent α. When Sis orthodox, α is necessarily medial (in the sense that x = xαx for every x ɛ 〈E〉) and αSα is uniquely unit orthodox. When S is orthodox and α is a middle unit (in the sense that xαy = xy for all x, y ɛ S), we obtain a structure theorem which generalises the description given in [2] for uniquely unit orthodox semigroups in terms of a semi-direct product of a band with a identity and a group. 
Blyth, T. S.; Giraldes, Emília; Marques-Smith, M. Paula O. Associate subgroups of orthodox semigroups. Glasgow mathematical journal, Tome 36 (1994) no. 2, pp. 163-171. doi: 10.1017/S0017089500030706
@article{10_1017_S0017089500030706,
     author = {Blyth, T. S. and Giraldes, Em{\'\i}lia and Marques-Smith, M. Paula O.},
     title = {Associate subgroups of orthodox semigroups},
     journal = {Glasgow mathematical journal},
     pages = {163--171},
     year = {1994},
     volume = {36},
     number = {2},
     doi = {10.1017/S0017089500030706},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500030706/}
}
TY  - JOUR
AU  - Blyth, T. S.
AU  - Giraldes, Emília
AU  - Marques-Smith, M. Paula O.
TI  - Associate subgroups of orthodox semigroups
JO  - Glasgow mathematical journal
PY  - 1994
SP  - 163
EP  - 171
VL  - 36
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500030706/
DO  - 10.1017/S0017089500030706
ID  - 10_1017_S0017089500030706
ER  - 
%0 Journal Article
%A Blyth, T. S.
%A Giraldes, Emília
%A Marques-Smith, M. Paula O.
%T Associate subgroups of orthodox semigroups
%J Glasgow mathematical journal
%D 1994
%P 163-171
%V 36
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500030706/
%R 10.1017/S0017089500030706
%F 10_1017_S0017089500030706

[1] 1.d'Alarcao, H., Factorizable as a finiteness condition, Semigroup Forum, 20 (1980), 281–282. Google Scholar | DOI

[2] 2.Blyth, T. S. and McFadden, R., Unit orthodox semigroups, Glasgow Math. J., 24 (1983), 39–42. Google Scholar

[3] 3.Blyth, T. S. and McFadden, R., On the construction of a class of regular semigroups, J. Algebra, 81 (1983), 1–22. Google Scholar | DOI

[4] 4.Goodearl, K. R., von Neumann regular rings, (Pitman, 1979), (second edition, Krieger, 1991). Google Scholar

Cité par Sources :