Geodesic
Commutative Non-Singular Semigroups
Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 263-265

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

It is well known (see [5]) that the maximal right quotient ring of a ring R is (von Neumann) regular if and only if R is (right) non-singular (every large right ideal is dense). In [8] it was shown that for a semigroup S, the regularity of Q(S), the maximal right quotient semigroup [7], is independent of the non-singularity of S. Nevertheless, right non-singular semigroups form an important class of semigroups. 
Jr., C. S. Johnson; McMorris, F. R. Commutative Non-Singular Semigroups. Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 263-265. doi: 10.4153/CMB-1977-040-5
@article{10_4153_CMB_1977_040_5,
     author = {Jr., C. S. Johnson and McMorris, F. R.},
     title = {Commutative {Non-Singular} {Semigroups}},
     journal = {Canadian mathematical bulletin},
     pages = {263--265},
     year = {1977},
     volume = {20},
     number = {2},
     doi = {10.4153/CMB-1977-040-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-040-5/}
}
TY  - JOUR
AU  - Jr., C. S. Johnson
AU  - McMorris, F. R.
TI  - Commutative Non-Singular Semigroups
JO  - Canadian mathematical bulletin
PY  - 1977
SP  - 263
EP  - 265
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-040-5/
DO  - 10.4153/CMB-1977-040-5
ID  - 10_4153_CMB_1977_040_5
ER  - 
%0 Journal Article
%A Jr., C. S. Johnson
%A McMorris, F. R.
%T Commutative Non-Singular Semigroups
%J Canadian mathematical bulletin
%D 1977
%P 263-265
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-040-5/
%R 10.4153/CMB-1977-040-5
%F 10_4153_CMB_1977_040_5

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

[2] 2. Hinkle, C. V. Jr., Generalized semigroups of quotients, Trans. Amer. Math. Soc. 183 (1973), 87-117. Google Scholar

[3] 3. Hinkle, C. V. Jr., The extended centralizer of an S-set, Pacific J. Math. 53 (1974), 163-170. Google Scholar

[4] 4. Johnson, C. S. Jr. and McMorris, F. R., Nonsingular semilattices and semigroups, Czech. Math. J. 26 (1976), 280-282. Google Scholar

[5] 5. Lambek, J., Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966. Google Scholar

[6] 6. Lopez, Antonio M. Jr. and Luedeman, John K., The bicommutator of the injective hull of a nonsingular semigroup, Semigroup Forum 12 (1976), 71-77. Google Scholar

[7] 7. McMorris, F. R., The maximal quotient semigroup, Semigroup Forum, 4 (1972), 360-364. Google Scholar

[8] 8. McMorris, F. R., The singular congruence and the maximal quotient semigroup, Canad. Math. Bull. 15 (1972), 301-303. Google Scholar

[9] 9. Rompke, Jurgen, Regular, commutative, maximal semigroups of quotients, Canad. Math. Bull. 18 (1975), 99-104. Google Scholar

Cité par Sources :