Commutative Non-Singular Semigroups
Carlos Johnson, Fred R. McMorris · Canadian Mathematical Bulletin · 1977
It is well known (see [5]) that the maximal right quotient ring of a ringRis (von Neumann) regular if and only ifRis (right) non-singular (every large right ideal is dense). In [8] it was shown that for a semigroupS, the regularity ofQ(S), the maximal right quotient semigroup [7], is independent of the non-singularity ofS. Nevertheless, right non-singular semigroups form an important class of semigroups.