Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T01:06:27.190Z Has data issue: false hasContentIssue false
  • English
  • Français

Semigroups with Quasi-Zeroes

Published online by Cambridge University Press:  20 November 2018

S. A. Rankin  and
C. M. Reis
S. A. Rankin
Affiliation:
University of Western Ontario, London, Ontario
C. M. Reis
Affiliation:
University of Western Ontario, London, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 3 , 01 June 1980 , pp. 511 - 530
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Demlovâ, M., On groups of units in a special class of monoids, Semigroup Foru. 16 (1978), 443–454.Google Scholar
2. Jones, W. P., Semigroups satisfying ring-like conditions, Ph.D. Thesis, Univ. of Iowa (1969).Google Scholar
3. Kim, J. B., No semigroup is a finite union of mutants, Semigroup Foru. 6 (1973), 360–361.Google Scholar
4. LaTorre, D. R., An internal characterization of the O-radical of a semigroup, Math. Nachr. 45 (1970), 279–281.Google Scholar
5. Oehmke, R. H., Quasi-regularity in semigroups, Séminaire Dubreil-Pisot (1969/70), Demigroups no. 1, 1-3.Google Scholar
6. Rankin, S., Reis, C. and Thierrin, G., Right local semigroups, J. of Alg. 46 (1977), 134–147.Google Scholar
7. Satyanarayana, M., On the O-radical of a semigroup, Math. Nachr. 66 (1975), 231–234.Google Scholar
8. Seidel, H., Über das Radikal einer Halbgruppe, Math. Nachr. 29 (1965), 255–263.Google Scholar
9. Thue, A., Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihe, Videnskabsselskabets Skrifter, I Mat. Nat. KL, Kristiania (1912), 1–67.Google Scholar