Cancellative Orders |
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Authors: | David Easdown Victoria Gould |
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Institution: | (1) School of Mathematics and Statistics, University of Sydney,;(2) Department of Mathematics, University of York, |
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Abstract: | left order in Q and Q is a semigroup of left quotients of S if every q∈Q can be written as q=a^*b for some a, b∈S where a^* denotes the inverse of a in a subgroup of Q and if,
in addition, every square-cancellable element of S lies in a subgroup of Q. Perhaps surprisingly, a semigroup, even a commutative
cancellative semigroup, can have non-isomorphic semigroups of left quotients. We show that if S is a cancellative left order
in Q then Q is completely regular and the {\cal D}-classes of Q are left groups. The semigroup S is right reversible and its
group of left quotients is the minimum semigroup of left quotients of S.
The authors are grateful to the ARC for its generous financial support. |
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Keywords: | |
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