Geodesic
Semigroups with Quasi-Zeroes
Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 511-530

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

Let S be a semigroup. An element a ∈ S is said to be a left quasi-zero if <a>x ⋂ <a> ≠ ∅ for all x ∈ S, where <a> denotes the cyclic sub-semigroup of S generated by a. In a recent study [6] of semigroups with a maximum right congruence, such elements proved to be useful in providing characterizations of these semigroups. Left quasizeroes have appeared in the literature under different names in a variety of situations. In the context of semigroup radicals, left quasi-zeroes are called right quasi-regular elements, where an element is defined to be right quasi-regular if it is not a left identity for any right congruence other than the universal congruence (see [4], [5], [2], [7], and [8]). 
Rankin, S. A.; Reis, C. M. Semigroups with Quasi-Zeroes. Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 511-530. doi: 10.4153/CJM-1980-040-x
@article{10_4153_CJM_1980_040_x,
     author = {Rankin, S. A. and Reis, C. M.},
     title = {Semigroups with {Quasi-Zeroes}},
     journal = {Canadian journal of mathematics},
     pages = {511--530},
     year = {1980},
     volume = {32},
     number = {3},
     doi = {10.4153/CJM-1980-040-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-040-x/}
}
TY  - JOUR
AU  - Rankin, S. A.
AU  - Reis, C. M.
TI  - Semigroups with Quasi-Zeroes
JO  - Canadian journal of mathematics
PY  - 1980
SP  - 511
EP  - 530
VL  - 32
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-040-x/
DO  - 10.4153/CJM-1980-040-x
ID  - 10_4153_CJM_1980_040_x
ER  - 
%0 Journal Article
%A Rankin, S. A.
%A Reis, C. M.
%T Semigroups with Quasi-Zeroes
%J Canadian journal of mathematics
%D 1980
%P 511-530
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-040-x/
%R 10.4153/CJM-1980-040-x
%F 10_4153_CJM_1980_040_x

[1] 1. Demlovâ, M., On groups of units in a special class of monoids, Semigroup Foru. 16 (1978), 443–454. Google Scholar

[2] 2. Jones, W. P., Semigroups satisfying ring-like conditions, Ph.D. Thesis, Univ. of Iowa (1969). Google Scholar

[3] 3. Kim, J. B., No semigroup is a finite union of mutants, Semigroup Foru. 6 (1973), 360–361. Google Scholar

[4] 4. LaTorre, D. R., An internal characterization of the O-radical of a semigroup, Math. Nachr. 45 (1970), 279–281. Google Scholar

[5] 5. Oehmke, R. H., Quasi-regularity in semigroups, Séminaire Dubreil-Pisot (1969/70), Demigroups no. 1, 1-3. Google Scholar

[6] 6. Rankin, S., Reis, C. and Thierrin, G., Right local semigroups, J. of Alg. 46 (1977), 134–147. Google Scholar

[7] 7. Satyanarayana, M., On the O-radical of a semigroup, Math. Nachr. 66 (1975), 231–234. Google Scholar

[8] 8. Seidel, H., Über das Radikal einer Halbgruppe, Math. Nachr. 29 (1965), 255–263. Google Scholar

[9] 9. Thue, A., Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihe, Videnskabsselskabets Skrifter, I Mat. Nat. KL, Kristiania (1912), 1–67. Google Scholar

Cité par Sources :