Geodesic
The Singular Congruence and the Maximal Quotient Semigroup
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 301-303

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

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. 
McMorris, F. R. The Singular Congruence and the Maximal Quotient Semigroup. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 301-303. doi: 10.4153/CMB-1972-056-8
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