On connections between Morita semigroups and strong Morita equivalence

Abstract

A surjective Morita context connecting semigroups S and T yields a Morita semigroup and a strict local isomorphism from it onto S along which idempotents lift. We describe strong Morita equivalence of firm semigroups in terms of Morita semigroups and isomorphisms. We also generalize some of Hotzel’s theorems to semigroups with weak local units. In particular, the Morita semigroup induced by a dual pair β over a semigroup with weak local units is isomorphic to ${\Sigma }^{\beta }$.

KEYWORDS:

• Dual pair
• Morita context
• Morita equivalence
• Morita semigroup
• Rees matrix semigroup

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20M30

Acknowledgments

I would like to thank the anonymous referee for their numerous suggestions and corrections regarding the history of Morita theory of semigroups.

Additional information

Funding

This work was partially supported by the Estonian Research Council Grant PRG1204.