Strong Morita Equivalence and a Generalisation of the Rees Theorem

✍ Scribed by S. Talwar

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 211 KB
• Volume: 181
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1996.0125

✦ Synopsis

In our earlier work we associated a natural category to a semigroup with local units and proved semigroup analogues of the celebrated Morita theorems for rings. In this article we use the notion of a Morita context to define an equivalence relation on a far wider class of semigroups. We give a semigroup analogue of Morita I and show that Morita equivalent semigroups can be constructed with ease. Our construction is based on the classical Rees theorem and a generalisation of this theorem by Hotzel. We then use properties of equivalent categories to deduce properties of this construction. Finally, we give a new generalisation of the Rees theorem and applications of this generalisation.