Geodesic
Extensions of One Primitive Inverse Semigroup by Another
Canadian journal of mathematics, Tome 24 (1972) no. 2, pp. 270-278

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

Every inverse semigroup containing a primitive idempotent is an ideal extension of a primitive inverse semigroup by another inverse semigroup. Consequently, in developing the theory of inverse semigroups, it is natural to study ideal extensions of primitive inverse semigroups (cf. [3; 7]). Since the structure of any primitive inverse semigroup is known, an obvious type of ideal extension to consider is that of one primitive inverse semigroup by another. In this paper, we will construct all such extensions and give an abstract characterization of the resulting semigroup.The problem of extending one primitive inverse semigroup by another can be essentially reduced to that of extending one Brandt semigroup by another Brandt semigroup. The latter problem has been solved by Lallement and Petrich in [3] in case the first Brandt semigroup has only a finite number of idempotents. 
Ault, Janet E. Extensions of One Primitive Inverse Semigroup by Another. Canadian journal of mathematics, Tome 24 (1972) no. 2, pp. 270-278. doi: 10.4153/CJM-1972-021-0
@article{10_4153_CJM_1972_021_0,
     author = {Ault, Janet E.},
     title = {Extensions of {One} {Primitive} {Inverse} {Semigroup} by {Another}},
     journal = {Canadian journal of mathematics},
     pages = {270--278},
     year = {1972},
     volume = {24},
     number = {2},
     doi = {10.4153/CJM-1972-021-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-021-0/}
}
TY  - JOUR
AU  - Ault, Janet E.
TI  - Extensions of One Primitive Inverse Semigroup by Another
JO  - Canadian journal of mathematics
PY  - 1972
SP  - 270
EP  - 278
VL  - 24
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-021-0/
DO  - 10.4153/CJM-1972-021-0
ID  - 10_4153_CJM_1972_021_0
ER  - 
%0 Journal Article
%A Ault, Janet E.
%T Extensions of One Primitive Inverse Semigroup by Another
%J Canadian journal of mathematics
%D 1972
%P 270-278
%V 24
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-021-0/
%R 10.4153/CJM-1972-021-0
%F 10_4153_CJM_1972_021_0

[1] 1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Math. Surveys No. 7 (Amer. Math. Soc, Providence, R.I.) Vol. I (1961), Vol. II (1967). Google Scholar

[2] 2. Gérard, Lallement and Mario, Petrich, Décompositions I-matricielles d'un demi-groupe, J. Math. Pures Appl. 45 (1966), 67–117. Google Scholar

[3] 3. Gérard, Lallement and Mario, Petrich, Extensions of a Brandt semigroup by another, Can. J. Math. 22 (1970), 974–983. Google Scholar

[4] 4. Mario, Petrich, The translational hull of a completely 0-simple semigroup, Glasgow Math. J. 9 (1968), 1–11. Google Scholar

[5] 5. Mario, Petrich, Translational hull and semigroups of binary relations, Glasgow Math. J. 9 (1968), 12–21. Google Scholar

[6] 6. Gábor, Szász, Introduction to lattice theory (Academic Press, New York, 1963). Google Scholar

[7] 7. Warne, R. J., Extensions of Brandt semigroups and applications, Illinois J. Math. 10 (1966), 652–660. Google Scholar

Cité par Sources :