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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.
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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

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Gluskin, L. M. (1960), ‘Ideals in rings and their multiplicative semigroups’, Uspedni Mat. Nauk. (N. S.) 15, No. 4 (94), 141–148;Google Scholar
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Satyanarayana, M. (1973), ‘On semigroups admitting ring structure II’, Semigroup Forum 6, 189–197.CrossRefGoogle Scholar