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 given right R-module M, so-called M-flat left R-modules are investigated, which
are flat relative to short exact sequences in the subcategory σ [M] subgenerated by M. The …

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 …

Let R be a ring and M a fixed right R-module. A new characterization of M-flatness is given
by certain linear equations. For a left R-module F such that the canonical map M⊗ RF→ …

Recently, Costa [4] introduced the concept of n-coherent rings. In this note we shall give
some further properties of n-coherent rings. Let R be a ring and na nonnegative integer …

Throughout this paper we assume that every ring has an identity. A ring S is called left (right)-
injective if it is a left (right)-injective S-module. A ring is called injective if it is left-and right …

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 …

This is of course equivalent to the condition that every simple module is either projective or
injective. Theorem 1.1 gives necessary and sufficient conditions for a T-ring to have property …

Let R be a ring with an identity 1, and R′ a ring anti-isomorphic to R. Let V be an R-module
as well as an R′-module. We assume that 1 a= a for all elements a in V and that V satisfies …

In 1974 Fuller characterized the equivalences between certain subcategories of thecategory
of modules over a ring and the category of unital modules over a ring with iden-tity. In this …