Geodesic
Generalized semigroups of quotients
Glasgow mathematical journal, Tome 12 (1971) no. 2, pp. 150-161

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Berthiaume, Pierre. Generalized semigroups of quotients. Glasgow mathematical journal, Tome 12 (1971) no. 2, pp. 150-161. doi: 10.1017/S0017089500001257
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