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Generalized semigroups of quotients

Published online by Cambridge University Press:  18 May 2009

Pierre Berthiaume
Pierre Berthiaume
Affiliation:
Université de Montréal, Montréal, Quebec, Canada
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In ([6]; pages 36–41), Lambek constructs the maximal ring of quotients Q(R) of a commutative ring R by denning a multiplication on Homr(D, R) where D ranges over all the dense ideals of R, and this generalizes the classical construction of ring of quotients, (cf. [6] for all the references on the subject.)

This programme is carried over, in the first section of this article, to the categoryof commutative reductive semigroups. Examples show that the maximal semigroup of quotients of a commutative monoid can be different from the classical one.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 12 , Issue 2 , September 1971 , pp. 150 - 161
Copyright
Copyright © Glasgow Mathematical Journal Trust 1971

References

REFERENCES

1.Berthiaume, P., The injective envelope of S-sets, Canad. Math. Bull. 10 (1967), 261–273.CrossRefGoogle Scholar
2.Berthiaume, P., Rational completions of monoids, Thesis, McGill University, 1964.Google Scholar
3.Brainerd, B. and Lambek, J., On the ring of quotients of a Boolean ring, Canad. Math. Bull. 2 (1959), 25–29.CrossRefGoogle Scholar
4.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Amer. Math. Soc. Mathematical Surveys 7, Vol. I (Providence, R.I., 1961).Google Scholar
5.Findlay, G. D. and Lambek, J., A generalized ring of quotients I, II, Canad. Math. Bull. 1 (1958), 77–85, 155–167.CrossRefGoogle Scholar
6.Lambek, J., Lectures on rings and modules (Waltham, Mass., 1966).Google Scholar
7.Lambek, J., on Utumi’s ring of quotients, Canad. J. Math. 15 (1963), 353–370.CrossRefGoogle Scholar
8.McMorris, F. R., The maximal quotient semigroup of a semigroup, Thesis, University of Wisconsin-Milwaukee, 1969.Google Scholar