Geodesic
Commutative Non-Singular Semigroups
Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 263-265

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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. 
Jr., C. S. Johnson; McMorris, F. R. Commutative Non-Singular Semigroups. Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 263-265. doi: 10.4153/CMB-1977-040-5
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     title = {Commutative {Non-Singular} {Semigroups}},
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     year = {1977},
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     doi = {10.4153/CMB-1977-040-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-040-5/}
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