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The Singular Congruence and the Maximal Quotient Semigroup

Published online by Cambridge University Press:  20 November 2018

F. R. McMorris
F. R. McMorris*
Affiliation:
Bowling Green State University, Bowling Green, Ohio
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It is a well known result (see [4, p. 108]) that if R is a ring and Q(R) its maximal right quotient ring, then Q(R) is (von Neumann) regular if and only if every large right ideal of R is dense. This condition is equivalent to saying that the singular ideal of R is zero. In this note we show that the condition loses its magic in the theory of semigroups.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 301 - 303
Copyright
Copyright © Canadian Mathematical Society 1972

References

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5. McMorris, F. R., The maximal quotient semigroup, Semigroup Forum (to appear).Google Scholar
6. McMorris, F. R., The quotient semigroup of a semigroup that is a semilattice of groups, Glasgow Math. J. 12, (1971), 18-23.Google Scholar