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Semigroups of right quotients of a semigroup which is a semilattice of groups

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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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References

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Authors and Affiliations

  1. Clemson University, 29631, Clemson, South Carolina

    C. V. Hinkle Jr.

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  1. C. V. Hinkle Jr.
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Communicated by M. Petrich

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Hinkle, C.V. Semigroups of right quotients of a semigroup which is a semilattice of groups. Semigroup Forum 5, 167–173 (1972). https://doi.org/10.1007/BF02572887

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  • DOI: https://doi.org/10.1007/BF02572887

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