Geodesic
On a Conjecture Concerning Semigroup Homomorphisms
Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 641-644

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

In this paper we settle (with a counterexample) the question raised by Clifford and Preston in [2, p. 275], concerning maximal group homomorphic images of semigroups. We also consider the question in a more general context and characterize all such examples. The notation and definitions follow [1; 2].By a type of semigroups we mean a class of semigroups, closed under isomorphisms and containing the one-element semigroup. If S is any semigroup and is a type, then a semigroup S* is defined, in [1, p. 18], to be a maximal homomorphic image of S having type if(i) ,(ii) S* is a homomorphic image of S, and(iii) whenever and T is a homomorphic image of S, then there exists a homomorphism from S* onto T. 
Plemmons, R. J. On a Conjecture Concerning Semigroup Homomorphisms. Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 641-644. doi: 10.4153/CJM-1970-070-4
@article{10_4153_CJM_1970_070_4,
     author = {Plemmons, R. J.},
     title = {On a {Conjecture} {Concerning} {Semigroup} {Homomorphisms}},
     journal = {Canadian journal of mathematics},
     pages = {641--644},
     year = {1970},
     volume = {22},
     number = {3},
     doi = {10.4153/CJM-1970-070-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-070-4/}
}
TY  - JOUR
AU  - Plemmons, R. J.
TI  - On a Conjecture Concerning Semigroup Homomorphisms
JO  - Canadian journal of mathematics
PY  - 1970
SP  - 641
EP  - 644
VL  - 22
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-070-4/
DO  - 10.4153/CJM-1970-070-4
ID  - 10_4153_CJM_1970_070_4
ER  - 
%0 Journal Article
%A Plemmons, R. J.
%T On a Conjecture Concerning Semigroup Homomorphisms
%J Canadian journal of mathematics
%D 1970
%P 641-644
%V 22
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-070-4/
%R 10.4153/CJM-1970-070-4
%F 10_4153_CJM_1970_070_4

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

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

[3] 3. Good, R. A. and Hughes, D. R., Associated groups for a semigroup, Bull. Amer. Math. Soc. 58 (1952), 264–265. Google Scholar

[4] 4. McAlister, D. B., A homomorphism theorem for semigroups, J. London Math. Soc. 43 (1968), 355–366. Google Scholar

[5] 5. Plemmons, R. J. and Tamura, T., Semigroups with a maximal homomorphic image having zero, Proc. Japan Acad. 41 (1965), 681–685. Google Scholar

[6] 6. Stoll, R. R., Homomorphisms of a semigroup onto a group, Amer. J. Math. 73 (1951), 475–481. Google Scholar

[7] 7. Tamura, T., Maximal or greatest homomorphic images of a given type, Can. J. Math. 20 (1968), 264–271. Google Scholar

Cité par Sources :