Geodesic
Inverse semigroups as extensions of semilattices
Glasgow mathematical journal, Tome 16 (1975) no. 1, pp. 12-21

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

Let S be an inverse semigroup with semilattice of idempotents E, and let ρ be a congruence on S. Then ρ is said to be idempotent-determined [2], or I.D. for short, if (a, b) ∈ р and a∈E imply that b ∈ E. If, further, ρ is a group congruence, then clearly ρ is the minimum group congruence on S, and in this case S is said to be proper [8]. Let T = S/ρ. 
O'Carroll, Liam. Inverse semigroups as extensions of semilattices. Glasgow mathematical journal, Tome 16 (1975) no. 1, pp. 12-21. doi: 10.1017/S0017089500002445
@article{10_1017_S0017089500002445,
     author = {O'Carroll, Liam},
     title = {Inverse semigroups as extensions of semilattices},
     journal = {Glasgow mathematical journal},
     pages = {12--21},
     year = {1975},
     volume = {16},
     number = {1},
     doi = {10.1017/S0017089500002445},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002445/}
}
TY  - JOUR
AU  - O'Carroll, Liam
TI  - Inverse semigroups as extensions of semilattices
JO  - Glasgow mathematical journal
PY  - 1975
SP  - 12
EP  - 21
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002445/
DO  - 10.1017/S0017089500002445
ID  - 10_1017_S0017089500002445
ER  - 
%0 Journal Article
%A O'Carroll, Liam
%T Inverse semigroups as extensions of semilattices
%J Glasgow mathematical journal
%D 1975
%P 12-21
%V 16
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002445/
%R 10.1017/S0017089500002445
%F 10_1017_S0017089500002445

[1] 1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vols. I and II, Math. Surveys of the American Math. Soc. 7 (Providence, R.I., 1961 and 1967). Google Scholar

[2] 2.Green, D. G., Extensions of a semilattice by an inverse semigroup, Bull. Austral. Math. Soc. 9 (1973), 21–31. Google Scholar | DOI

[3] 3.McAlister, D. B., Groups, semilattices and inverse semigroups II, Trans. Amer. Math. Soc.; to appear. Google Scholar

[4] 4.O'Carroll, L., A class of congruences on a posemigroup, Semigroup Forum 3 (1971), 173–179. Google Scholar | DOI

[5] 5.O'Carroll, L., Reduced inverse and partially ordered semigroups, J. London Math. Soc. (I), 9 (1974), 293–301. Google Scholar | DOI

[6] 6.O'Carroll, L., Embedding theorems for proper inverse semigroups, J. of Algebra; submitted. Google Scholar

[7] 7.Reilly, N. R., Inverse semigroups of partial transformations and θ-classes, Pac. J. Math. 41 (1972), 215–235. Google Scholar | DOI

[8] 8.Saito, T., Proper ordered inverse semigroups, Pac. J. Math. 15 (1965), 649–666. Google Scholar

[9] 9.Schein, B. M., Completions, translational hulls, and ideal extensions of inverse semigroups, Czech. Math. J. 23 (98) (1973), 575–610. Google Scholar | DOI

Cité par Sources :