David Easdown and Victoria Gould
Research Report 96-2
To appear in Semigroup Forum
Date: December 1995
A subsemigroup S of a semigroup Q is a left order in Q and Q is a
semigroup of left quotients of S if every q in Q can be written as
q=a*b for some a,b in 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
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
cancellative semigroups of left quotients. completely regular semigroups.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics