It is proved that a ring R is right perfect if and only if it is Σ-cotorsion as a right module over
itself. Several other conditions are shown to be equivalent. For example, that every pure …

We study coherence properties of a module M over its endomorphism ring. Hereby we
extend to modules known characterizations of coherent and π-coherent rings. Moreover, we …

arXiv:2403.07619v1 [math.RA] 12 Mar 2024 Page 1 arXiv:2403.07619v1 [math.RA] 12 Mar
2024 SIMPLE-MINDED SYSTEMS AND COHERENT RINGS ZHEN ZHANG Abstract. Let A be a …

By using the correspondence between locally finitely presented additive categories and
rings with enough idempotents, we study several properties of such rings in terms of the …

Let M be a right R-module with S= End (MR). Given two cardinal numbers α and β and a row-
finite matrix A∈ RFM β× α (S), SM is called injective relative to A if every left S …

Let N be a left R-module with the endomorphism ring S= End (RN). Given two cardinal
numbers α and β and a matrix A∈ S β× α, N is called flat relative to A in case, for each x∈ lN …

R is called a left PS (resp. left min-coherent, left universally mininjective) ring if every simple
left ideal is projective (resp. finitely presented, a direct summand of R). We first investigate …

Let m and n be fixed positive integers. R is called a right (m, n)-injective ring if every right R-
homomorphism from an n-generated submodule of the right R-module R m to R extends to …

A ring is called right P-coherent if every principal right ideal is finitely presented. Let MR be a
right R-module. We study the P-coherence of the endomorphism ring S of MR. It is shown …