In this paper, we classify additive closed symmetric monoidal structures on the category of
left R-modules by using Watts' theorem. An additive closed symmetric monoidal structure is …

ON MODULES OVER FORMAL TRIANGULAR MATRIX RINGS | East West Math Skip to main
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Let R be a ring, n, d be fixed non-negative integers, the class of (n, d)-injective left R-
modules, and the class of (n, d)-flat right R-modules. In this paper, we prove that if R is a left …

Abstract Suppose that T=(A 0 UB) is a formal triangular matrix ring, where A and B are rings
and U is a (B, A)-bimodule. We first study how to construct duality pairs of T-modules using …

Let R be a commutative ring with identity and S a multiplicative subset of R. The aim of this
paper is to study the class of commutative rings in which every S-flat module is flat (resp …

In this paper we carry out a systematic study of modules over a formal triangular matrix ring
[Formula: see text] Using the alternative description of right T-modules as triples (X, Y) f with …

In this paper we describe the structure of prime and semiprime R-modules M such that
R/AnnR (M) is artinian. The obtained results are then applied to describe the structure of …

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. Let℘ be the class of all singular simple …

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 …

Throughout this paper R will be a commutative ring with 1. The purpose of this paper is to
provide two new characterizations of coherent rings. The first of these characterizations …