Abstract
Let S be a semigroup with zero which is a semilattice of groups. In [6], McMorris showed that the semigroup of quotients Q=Q(S) corresponding to the filter of “dense” right ideals of the semigroup S is also a semilattice of groups. He accomplished this by noting that Q is a regular semigroup in which all idempotents are central, an equivalent formulation of a semilattice of groups. In this paper we develop the semigroup of quotients Q corresponding to an arbitrary right quotient filter on S (as defined herein) and note the above result in this more general setting by explicitly constructing a semigroup which is isomorphic to Q. We also see that the underlying semilattice for Q in this case is isomorphic to a semigroup of quotients of the original semilattice for the semigroup S.
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