Cancellative Orders

Authors

David Easdown and Victoria Gould

Status

Research Report 96-2
To appear in Semigroup Forum
Date: December 1995

Abstract

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
Secondary:

Content

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