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Commutative Non-Singular Semigroups

Published online by Cambridge University Press:  20 November 2018

C. S. Johnson Jr.  and
F. R. McMorris
C. S. Johnson Jr.
Affiliation:
Dept. of Math., Bowling Green State University, Bowling GreenOhio 43403 U.S.A.
F. R. McMorris
Affiliation:
Dept. of Math., Bowling Green State University, Bowling GreenOhio 43403 U.S.A.
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It is well known (see [5]) that the maximal right quotient ring of a ring R is (von Neumann) regular if and only if R is (right) non-singular (every large right ideal is dense). In [8] it was shown that for a semigroup S, the regularity of Q(S), the maximal right quotient semigroup [7], is independent of the non-singularity of S. Nevertheless, right non-singular semigroups form an important class of semigroups.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 2 , 01 June 1977 , pp. 263 - 265
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Amer. Math. Soc. Surveys, No. 7, Vol. I, Providence, R.I., 1961.Google Scholar
2. Hinkle, C. V. Jr., Generalized semigroups of quotients, Trans. Amer. Math. Soc. 183 (1973), 87-117.Google Scholar
3. Hinkle, C. V. Jr., The extended centralizer of an S-set, Pacific J. Math. 53 (1974), 163-170.Google Scholar
4. Johnson, C. S. Jr. and McMorris, F. R., Nonsingular semilattices and semigroups, Czech. Math. J. 26 (1976), 280-282.Google Scholar
5. Lambek, J., Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966.Google Scholar
6. Lopez, Antonio M. Jr. and Luedeman, John K., The bicommutator of the injective hull of a nonsingular semigroup, Semigroup Forum 12 (1976), 71-77.Google Scholar
7. McMorris, F. R., The maximal quotient semigroup, Semigroup Forum, 4 (1972), 360-364.Google Scholar
8. McMorris, F. R., The singular congruence and the maximal quotient semigroup, Canad. Math. Bull. 15 (1972), 301-303.Google Scholar
9. Rompke, Jurgen, Regular, commutative, maximal semigroups of quotients, Canad. Math. Bull. 18 (1975), 99-104.Google Scholar