We introduce and study the c. Noetherian dimension of an R− module A, denoted by cn−
dim (A), which is the Noetherian dimension of the partially ordered set (briefly, poset) of …

We introduce and study the concept of small Krull dimension of a module which is Krull-like
dimension extension of the concept of DCC on small submodules. Using this concept we …

This text is an expanded version of the Lecture Notes [15] of a minicourse that has been
given by the author at the XXIII Escola de Álgebra, Universidade Estadual de Maringá, July …

‎ 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 …

In this article, we study modules with chain condition on non-finitely generated submodules.
We show that if an R-module M satisfies the ascending chain condition on non-finitely …

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 …

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, 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 prove the result in the title. We study submodules $ N $ of a module $ M $ such that
whenever $\frac {M}{N} $ satisfies the double infinite chain condition so does $ M …

‎ It is shown that‎‎ if $ M $ is an Artinian module over a ring‎‎ $ R $‎,‎ then $ M $ has Noetherian
dimension $\alpha $‎,‎ where $\alpha $ is a countable ordinal number‎,‎ if and only if …