The fimdam al result of AV Jategaonkar's im ortant paper is th, e following: If is a finitely
generated Noetherian ring, and) r is an essential submoduie of ml! dimens~ Q~ 4.2, then M …

On Finitely Generated Modules Over Noetherian Rings Page 1 ON FINITELY GENERATED
MODULES OVER NOETHERIAN RINGS BY JP JANS(Q) 0. Introduction. If A is a module over a …

The purpose of this note is to prove the following result. Theorem 1. Let n be an integer
greater than zero. There exists a prime Noetherian ring R of Krull dimension n+ 1 and a …

This paper essentially deals with the following question: Over what rings are all modules
with Krull dimension (as defined in [1]; Gordon-Robson AMS memoirs) noetherian. The …

The Eakin-Nagata theorem says that if $ T $ is a commutative Noetherian ring which is
finitely generated as a module over a subring $ R $, then $ R $ is also Noetherian. This …

Introduction In this discussion every module over a ring R will be understood to be a left i2-
module. R will always have a unit, and every module will be unitary. The aim of this paper is …

The main result in this note (Corollary 1.5) shows that in a simple right Noetherian ring of
Krull dimension n, any right ideal can be generated by n+ 1 elements, one of which may be …

Introduction* The concept of the" injective envelope" of a module was first given by Eckmann
and Schopf [2], although this terminology was first employed by Matlis [5]. The injective …

Throughout this paper is a twosided noetherian ring and mod the category of finitely
generated-modules. For each integer k) 0 we k Ž. denote by mod the full subcategory of mod …

Throughout, R denotes an associative ring with identity, modules are unitary left R-modules.
A descending chain C of non-zero submoduies of a noethcrian module M is well-ordered …