It is shown that if e is an idempotent in a ring R such that both eRe and (1− e) R (1− e) are
clean rings, then R is a clean ring. This implies that the matrix ring M n (R) over a clean ring …

Since the discovery of the existence of the injective hull of an arbitrary module
independently in 1952 by Shoda and in 1953 by Eckmann and Schopf, there have been …

Matrices play an important role in both pure and applied mathematics. Matrices with entries
in rings have been intensively studied and used (eg, see [22, 87]); as well as matrices with …

In this paper we will describe the general form of commuting mappings of a class called
generalized matrix algebras and consider the question of when all commuting mappings of …

A ring is left Gorenstein regular if the classes of left modules with finite projective dimension
and finite injective dimension coincide and the injective and projective finitistic left …

This article concerns mainly on various ring properties of Morita contexts. Necessary and
sufficient conditions are obtained for a general Morita context or a trivial Morita context or a …

This work contains some new and known results on modules over formal matrix rings. The
main results are presented with proofs. In ring theory, various matrix rings play an important …

Abstract Let T=(A 0 UB) be a formal triangular matrix ring, where A and B are rings and U is
a (B, A)-bimodule. Let C 1 and C 2 be two classes of left A-modules, D 1 and D 2 be two …

The problem of diagonalization of matrices is a classic one. Its prototype is the Gauss
theorem on the equivalence of arbitrary matrix over the field to a diagonal matrix with ones …

Abstract Let T=(A 0 UB) be a formal triangular matrix ring, where A and B are rings and U is
a (B, A)-bimodule. We prove that, if T is a right coherent ring, UB has finite flat dimension, UA …