This paper is a continuation of our previous article [9]. We introduce an “artinian dimension”
of modules, which allows us to study isoartinian modules, and an “isoradical” of a module …

Abstract Let gm= sl (2)⋉ V (m), m≥ 1, where V (m) is the irreducible sl (2)-module of
dimension m+ 1 viewed as an abelian Lie algebra. It is known that the isomorphism classes …

‎ 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 …

Given a sequence d→=(d 1,…, dk) of natural numbers, we consider the Lie subalgebra h of
gl (d, F), where d= d 1+⋯+ dk and F is a field of characteristic 0, generated by two block …

In this paper, we define and study a valuation dimension for commutative rings. The
valuation dimension is a measure of how far a commutative ring deviates from being …

We counting valuation dimension of the ring Zn. Recently, Ghorbani and Nazemian
introduced the notion of a valuation dimension of a commutative rings that measures of how …

We present some methods for calculating the module's uniserial dimension that finitely g
enerated o ver a DVD in this article. The idea of a module's uniserial dimension over a …

Abstract Let\(\mathfrak {sl}(2)< imes {\mathfrak {h}} _n\),\(n\ge 1\), be the Galilean Lie algebra
over a field of characteristic zero, here\({\mathfrak {h}} _ {n}\) is the Heisenberg Lie algebra …

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 …

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 …