Morita Equivalence of Semigroups with Locally Commuting Idempotents

Abstract

We characterize those semigroups with local units which are Morita equivalent to semigroups with local units having commuting idempotents. A key element in this characterization is a description of those inverse categories which are equivalent to Cauchy completions of inverse semigroups.

Key Words:

• Commuting idempotents
• Inverse categories
• Morita theory
• Semigroups

2000 Mathematics Subject Classification:

• Primary 20M18
• Secondary 18B25, 18B40

ACKNOWLEDGMENTS

The first author would like to thank Aleppo University, Syria, and the British Council for their support. The second author would like to thank Lauri Tart for an e-mail that led him to simplify the definition of local isomorphism. Both authors would like to thank Professors Valdis Laan and Laci Márki for generously sharing their ideas on the Morita theory of semigroups, and the anonymous referee for his or her detailed comments and suggestions.

Notes

Communicated by V. Gould.