Morita-like equivalence of infinite matrix subrings
Let \(\Gamma\) be an arbitrary index set, \(R\) a ring with 1. If \(T\) is the ring of row-finite \(\Gamma \times \Gamma\) matrices over \(R\) which have only finitely many non-zero columns, and \(\ell^ 2 = \ell \in T\) satisfies \(T\ell T = T\), then the categories of unitary right modules over \(T\) and \(S = \ell T\ell\), respectively, are equivalent in view of Theorem 3.2, the main result of the paper. Here a right \(T\)-module \(M\) is called unitary if \(MT = M\) holds.
scientific article; zbMATH DE number 571355