Noetherian PI rings not module-finite over any commutative subring

NONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS

In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...

Superdecomposable pure injective modules over commutative Noetherian rings

We investigate width and Krull–Gabriel dimension over commutative Noetherian rings which are “tame” according to the Klingler–Levy analysis in [4], [5] and [6], in particular over Dedekind-like rings and their homomorphic images. We show that both are undefined in most cases.

D-Bases for Polynomial Ideals over Commutative Noetherian Rings

Contravariantly Finite Resolving Subcategories over Commutative Rings

Contravariantly finite resolving subcategories of the category of finitely generated modules have been playing an important role in the representation theory of algebras. In this paper we study contravariantly finite resolving subcategories over commutative rings. The main purpose of this paper is to classify contravariantly finite resolving subcategories over a henselian Gorenstein local ring;...

Noetherian rings without finite normalization

A number of examples and constructions of local Noetherian domains without finite normalization have been exhibited over the last seventy-five years. We discuss some of these examples, as well as the theory behind them.