×

Morita equivalence for rings without identity. (English) Zbl 0627.16031

Inspired by the work of G. D. Abrams [Commun. Algebra 11, 801-837 (1983; Zbl 0503.16034)], the authors develop a theory of Morita equivalence for certain rings without identity called rings with local units. Their main results characterize the corresponding equivalences in a way similar to the classical Morita theory, by showing that they are induced by a unitary balanced bimodule \({}_ RP_ S\) such that \({}_ RP\) and \(P_ S\) are locally projective generators. In the last part of the paper some examples are given which show, among other things, that the class of rings with local units is wider than the one considered by Abrams and there is also a description of the rings with local units which are Morita equivalent to division rings or primary rings.
Reviewer: J.L.Gómez Pardo

MSC:

16D90 Module categories in associative algebras

Citations:

Zbl 0503.16034
Full Text: DOI