Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T09:01:55.951Z Has data issue: false hasContentIssue false
  • English
  • Français

Semigroups in rings

Published online by Cambridge University Press:  09 April 2009

J. Cresp  and
R. P. Sullivan
J. Cresp
Affiliation:
University of Western AustraliaNedlands W.A. 6009, Australia.
R. P. Sullivan
Affiliation:
University of Western AustraliaNedlands W.A. 6009, Australia.
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.

A subset S of a ring R is a left semigroup ideal of R if RS ⊈ R, and a left ring ideal of R if in addition S is a subring of R. Gluskin (1960) investigated those rings with 1 which possess the property: (λ) every left semigroup ideal is a left ring ideal.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 2 , September 1975 , pp. 172 - 177
Copyright
Copyright © Australian Mathematical Society 1975

References

Burton, D. M. (1970), A first course in the theory of rings and ideals (Addison-Wesley, London, 1970).Google Scholar
Gluskin, L. M. (1960), ‘Ideals in rings and their multiplicative semigroups’, Uspedni Mat. Nauk. (N. S.) 15, No. 4 (94), 141–148;Google Scholar
translated in Amer. Math. Soc. Translations, 27 (2) (1963), 297–304.CrossRefGoogle Scholar
Peinado, R. E. (1970), ‘On semigroups admitting ring structure’, Semigroup Forum I, 189–208.CrossRefGoogle Scholar
Satyanarayana, M. (1971), ‘On semigroups admitting ring struct-ure’, Semigroup Forum 3, 43–50.CrossRefGoogle Scholar
Satyanarayana, M. (1973), ‘On semigroups admitting ring structure II’, Semigroup Forum 6, 189–197.CrossRefGoogle Scholar