Cancellative Orders


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 of S.

Key phrases

cancellative semigroups of left quotients. completely regular semigroups.

AMS Subject Classification (1991)

Primary: 20M10


The paper is available in the following forms:
TeX dvi format:
1996-2.dvi.gz (21kB) or 1996-2.dvi (52kB)

PostScript: (48kB) or (161kB)

To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it.

Sydney Mathematics and Statistics