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 …

In this paper, we introduce and study the concepts of non-essential Krull dimension and non-
essential Noetherian dimension of an R-module, where R is an arbitrary associative ring …

We define and study local dimension for coatomic modules. Local dimension is a measure
of how far a coatomic module deviates from being local. Every Noetherian module has local …

In this article, we introduce and study the concepts of quasi-Krull dimension and quasi-
Noetherian dimension of an R-module, where R is an arbitrary associative ring. These …

‎ 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 …

We denote by 𝒜 (R) the class of all Artinian R-modules and by 𝒩 (R) the class of all
Noetherian R-modules. It is shown that 𝒜 (R)⊆ 𝒩 (R)(𝒩 (R)⊆ 𝒜 (R)) if and only if 𝒜 (R/P)⊆ …

It is shown that a module M has countable Noetherian dimension if and only if the lengths of
ascending chains of submodules of M has a countable upper bound. This shows in …

Abstract Dimensions like Gelfand, Krull, Goldie have an intrinsic role in the study of theory of
rings and modules. They provide useful technical tools for studying their structure. We define …

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 …

In this paper, all rings are commutative with identity and all modules are unitary. Let R be a
ring and M an R-module. A proper submodule N of M is said to be prime (or P-prime) if rm …