We introduce and study the concept of dual perfect dimension which is a Krull-like
dimension extension of the concept of acc on finitely generated submodules. We observe …

We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals
the supremum of the flat (or (FP–) injective) dimensions of the simple R-modules;(b) if R is …

This paper is concerned with rings for which all modules in one of the following classes are
injective: simple modules, quasi-injective modules, or proper cyclic modules. Such rings are …

We introduce and investigate the notion of envelope dimension of commutative rings and
modules over them. In particular, we show that the envelope dimension of a ring,. We also …

Until now there has been no suitable dimension to measure how far a module deviates from
being uniserial. We define and study a new dimension, which we call uniserial dimension …

Let R be a ring and let S be a multiplicative subset of R. An R‐module M is said to be au‐S‐
absolutely pure module if Ext R 1 N, M is u‐S‐torsion for any finitely presented R‐module N …

In this paper, the notion of weak Krull dimension over any commutative ring is introduced
and the relations among Krull dimension, weak Krull dimension, weak global dimension …

Throughout this note, R stands for a ring with identity and all modules are unital modules. In
this note, for a given module M, we say that M has dominant dimension at least ny written …

‎ In this article‎,‎ we first‎‎ show that non-Noetherian Artinian uniserial modules over‎‎
commutative rings‎,‎ duo rings‎,‎ finite $ R $-algebras and right‎‎ Noetherian rings are $1 …

A ring is called $ n $-perfect ($ n\geq 0$), if every flat module has projective dimension less
or equal than $ n $. In this paper, we show that the $ n $-perfectness relate, via homological …