Geodesic
Certain fundamental congruences on a regular semigroup†
Glasgow mathematical journal, Tome 7 (1966) no. 3, pp. 145-159

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

In recent developments in the algebraic theory of semigroups attention has been focussing increasingly on the study of congruences, in particular on lattice-theoretic properties of the lattice of congruences. In most cases it has been found advantageous to impose some restriction on the type of semigroup considered, such as regularity, commutativity, or the property of being an inverse semigroup, and one of the principal tools has been the consideration of special congruences. For example, the minimum group congruence on an inverse semigroup has been studied by Vagner [21] and Munn [13], the maximum idempotent-separating congruence on a regular or inverse semigroup by the authors separately [9, 10] and by Munn [14], and the minimum semilattice congruence on a general or commutative semigroup by Tamura and Kimura [19], Yamada [22], Clifford [3] and Petrich [15]. In this paper we study regular semigroups and our primary concern is with the minimum group congruence, the minimum band congruence and the minimum semilattice congruence, which we shall consistently denote by α β and η respectively. 
Howie, J. M.; Lallement, G. Certain fundamental congruences on a regular semigroup†. Glasgow mathematical journal, Tome 7 (1966) no. 3, pp. 145-159. doi: 10.1017/S2040618500035334
@article{10_1017_S2040618500035334,
     author = {Howie, J. M. and Lallement, G.},
     title = {Certain fundamental congruences on a regular semigroup{\textdagger}},
     journal = {Glasgow mathematical journal},
     pages = {145--159},
     year = {1966},
     volume = {7},
     number = {3},
     doi = {10.1017/S2040618500035334},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500035334/}
}
TY  - JOUR
AU  - Howie, J. M.
AU  - Lallement, G.
TI  - Certain fundamental congruences on a regular semigroup†
JO  - Glasgow mathematical journal
PY  - 1966
SP  - 145
EP  - 159
VL  - 7
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S2040618500035334/
DO  - 10.1017/S2040618500035334
ID  - 10_1017_S2040618500035334
ER  - 
%0 Journal Article
%A Howie, J. M.
%A Lallement, G.
%T Certain fundamental congruences on a regular semigroup†
%J Glasgow mathematical journal
%D 1966
%P 145-159
%V 7
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S2040618500035334/
%R 10.1017/S2040618500035334
%F 10_1017_S2040618500035334

[1] 1.Clifford, A. H., Semigroups admitting relative inverses, Ann. of Math. 42 (1941), 1037–1049. Google Scholar | DOI

[2] 2.Clifford, A. H., Bands of semigroups, Proc. Amer. Math. Soc. 5 (1954), 499–504. Google Scholar | DOI

[3] 3.Clifford, A. H., Review of Yamada's paper [22], Math. Rev. 17 (1956), 584. Google Scholar

[4] 4.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, American Mathematical Society Mathematical Surveys No. 7, Vol. 1 (Providence, R. I., 1961). Google Scholar

[5] 5.Dubreil, P., Contribution à la théorie des demi-groupes, Mém. Acad. Sci. Inst. France (2) 63 (1941), no. 3, 1–52. Google Scholar

[6] 6.Fantham, P. H. H., On the classification of a certain type of semigroup, Proc. London Math. Soc. (3) 10 (1960), 409–427. Google Scholar | DOI

[7] 7.Green, J. A., On the structure of semigroups, Ann, of Math. 54 (1951), 163–172. Google Scholar | DOI

[8] 8.Green, J. A. and Rees, D., On semigroups in which x r = x, Proc. Cambridge Philos. Soc. 48 (1952), 35–40. Google Scholar | DOI

[9] 9.Howie, J. M., The maximum idempotent-separating congruence on an inverse semigroup Proc. Edinburgh Math. Soc. 14 (1964), 71–79. Google Scholar | DOI

[10] 10.Lallement, G., Congruences et équivalences de Green sur un demi-groupe régulier (to appear). Google Scholar

[11] 11.McLean, D., Idempotent semigroups, Amer. Math. Monthly 61 (1954), 110–113. Google Scholar | DOI

[12] 12.Miller, D. D. and Clifford, A. H., Regular -classes in semigroups, Trans. Amer. Math. Soc. 82 (1956), 270–280. Google Scholar

[13] 13.Munn, W. D., A class of irreducible matrix representations of an arbitrary inverse semigroup, Proc. Glasgow Math. Assoc. 5 (1961), 41–48. Google Scholar | DOI

[14] 14.Munn, W. D., A certain sublattice of the lattice of congruences on a regular semigroup, Proc. Cambridge Philos. Soc. 60 (1964), 385–391. Google Scholar | DOI

[15] 15.Petrich, Mario, The maximal semilattice decomposition of a semigroup, Math. Zeit. 85 (1964), 68–82. Google Scholar | DOI

[16] 16.Preston, G. B., Inverse semi-groups, J. London Math. Soc. 29 (1954), 396–403. Google Scholar | DOI

[17] 17.Preston, G. B., Congruences on Brandt semigroups, Math. Ann. 139 (1959), 91–94. Google Scholar | DOI

[18] 18.Rees, D., On semi-groups, Proc. Cambridge Philos. Soc. 36 (1940), 387–400. Google Scholar | DOI

[19] 19.Tamura, T. and Kimura, N., On decompositions of a commutative semigroup, Kodai Math. Sem. Rep. 4 (1954), 109–112. Google Scholar

[20] 20.Teissier, Marianne, Sur les équivalences régulières dans les demi-groupes, C. R. Acad. Sci. Paris 232 (1951), 1987–1989. Google Scholar

[21] 21.Vagner, V. V., The theory of generalised groups and generalised heaps, Mat. Sborn. (N. S.) 32 (1953), 545–632 (Russian). Google Scholar

[22] 22.Yamada, M., On the greatest semilattice decomposition of a semigroup, Kodai Math. Sem. Rep. 7 (1955), 59–62. Google Scholar | DOI

Cité par Sources :