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 …

Let R be a commutative, local, and principal ideal ring with maximal ideal m and residue
class field F. Suppose that every element of 1+ m is square. Then the problem of classifying …

In this article, first we find the number of idempotents and the zero-divisors of a matrix ring
over a finite field F. Next, given the order of the Jacobson radical of the finite unital ring R, we …

An associative ring R with identity is a generalized matrix ring with idempotent set E if E is a
finite set of orthogonal idempotentsof R whose sum is 1. We show that, in the presence of …

In this paper we introduce full elements in regular rings, and show that every matrix over
regular rings admits a diagonal reduction by full matrices. Also we get that a regular ring $ R …

Given a ring R and an integer n> _ 1 we have shown in [1] that there exists a commutative
ring S and a homomorphism p: R--~ Ma (S), the matrix rings over S, such that every other …

In the paper [1] Ābrams made a first step in extending the theory of Morita equivalence to
rings without identity. He considered rings in which a set of commuting idempotents is given …

In this paper, R always denotes a commutative ring with identity. The ideal of nHpotents and
the Jacobson radical of the ring R are denoted by N (R) and J (R), respectively. The vector [a …

arXiv:2204.13332v4 [math.RA] 31 Aug 2022 Page 1 arXiv:2204.13332v4 [math.RA] 31 Aug 2022
Automorphisms of Formal Matrix Rings Piotr Krylov, National Research Tomsk State University …

Similarity of Matrices Over Commutative Rings Page 1 Similarity of Matrices Over
Commutative Rings Robert M. Guralnick* Department of Mathematics University of Southern …