If $ R $ is a triangular $2\times 2$ matrix ring, the columns $ P $ and $ Q $ are fg projective $
R $-modules. We describe the universal localization of $ R $ which makes invertible an $ R …

Let $ T $ be the upper triangular matrix ring defined by a pair of rings $ R $ and $ S $ and an
$ RS $-bimodule $ M $. We use the QP definition of algebraic $ K $-theory to give a quick …

Let R be a ring and β× α (R)(ℝ β× α (R)) the set of all β× α full (row finite) matrices over
R where α and β≥ 1 are two cardinal numbers. A left R-module M is said to be “injective …

For a fixed integer n≧ 1, and a given ring R there exists a homomorphism ρ; R→ M n (K), K
a commutative ring such that every homomorphism of R into an n× n matrix ring M n (H) over …

1. Introduction. When R is a ring with identity, it is well known (and easy to show) that the nxn
matrix ring over the mxm matrix ring over R is isomorphic to the mn x mn matrix ring over R …

K. Morita has shown that, given two rings R and S, there is an isomorphism between the
category of left R-modules and the category of left S-modules if and only if there exists an RS …

We assume throughout that R is an associative ring with unity whose modules are left unital;
J (R) is the Jacobson radical of R;~ n is the ring of matrices of order n over the ideal~ of R; …

Recently ([1], Theorem 1;[2], Proposition 2;[3], Theorem 3.4;[4], p. 57, prob. 7) several
authors have shown that if R is a ring containing a unit, and Rn, the ring of n• n matrices over …

Let V n (R n) be the universal ring with respect to embeddings of the matrix ring R n into n× n
matrix rings over commutative rings. A construction and a representation is given for this …

ON THE REPRESENTATION THEORY OF RINGS IN MATRIX FORM Page 1 PACIFIC
JOURNAL OF MATHEMATICS Vol. 100, No. 1, 1982 ON THE REPRESENTATION THEORY …