Actions of Inverse Semigroups on Algebras

Abstract

In this article we prove that if S is a faithfully projective R-algebra and H is a finite inverse semigroup acting on S as R-linear maps such that the fixed subring S ^H  = R, then any partial isomorphism between ideals of S which are generated by central idempotents can be obtained as restriction of an R-automorphism of S and there exists a finite subgroup of automorphisms G of S with S ^G  = R.

Key Words:

• Inverse semigroup
• Partial action
• Weakly Galois extension

2000 Mathematics Subject Classification:

• Primary 16S29
• 16W22
• Secondary 20M30
• 47D03

ACKNOWLEDGMENT

This article was partially supported by CNPq and FAPERGS (Brazil).

Notes

Communicated by R. Wisbauer.