The global dimension gldim (R) of a Noetherian ring R, while a useful invariant when finite,
is often infinite. Several homological dimensions have been introduced to handle rings of …

Let R be a commutative Noetherian ring. If cmd R≤ 1, then it is shown that for any R-module
the large restricted injective dimension is a refinement of the Gorenstein injective dimension …

If $ R $ is a Noetherian ring and $ n $ is a positive integer, then there are only finitely many
ideals $ I $ of $ R $ such that the residue class ring $ R/I $ has cardinality $\leq n $. If $ R …

In this article, we introduce the concept of parallel Krull dimension of a module (briefly, p.
Krull dimension), which is Krull-like dimension extension of the concept of DCC on poset of …

Let A be a noetherian Auslander regular ring and δ the canonical dimension function on A-
modules, which is defined as δ (M)= d− j (M) where d is the global dimension of A and j (M) …

Throughout this paper, R denotes a commutative ring and M an Artinian R-module. The
concept of Krull dimension for Artinian modules M was introduced first by RN Roberts in [10] …

The flat dimensions of injective modules Page 1 manuscripta math. 78, 165- 177 (1993)
manuscripta mathematica Spfinger-Verlag 1~3 THE FLAT DIMENSIONS OF INJECTIVE …

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

The notion of Krull dimension of an R-module which is now one of the basic tools in the
theory of right Noetherian rings, see [5],[9] and [19], was first introduced by Rentschler and …

Let R be a commutative ring with identity. We show that the Krull dimension of the power
series ring R [X] can be uncountably infinite, ie, there exists an uncountably infinite chain of …