This volume provides a comprehensive introduction to module theory and the related part of
ring theory, including original results as well as the most recent work. It is a useful and …

This book surveys more than 125 years of aspects of associative algebras, especially ring
and module theory. It is the first to probe so extensively such a wealth of historical …

The purpose of this paper is to introduce two new classes of rings that is closely related to
the classes of piecewise Noetherian domains and piecewise w-Noetherian domains. Let …

Les systèmes localisants, les topologies de Gabriel, et les théories de torsion héréditaire
sont des notions équivalentes et ont été étudiés à partir des années 1960 pour étendre au …

A module $ M $ over a ring $ R $ is said to satisfy (accr) if the ascending chain of residuals
of the form $ N: B\subseteq N:{B^ 2}\subseteq N:{B^ 3}\subseteq\cdots $ terminates for every …

We prove that for a commutative integral domain R the following conditions are
equivalent:(a) R is a Prüfer domain with no non-zero idempotent prime ideals;(b) there is a …

For a property X of integral domains, D is said to be an MZ-X domain if DP has the property
X for all associated prime ideals P of an integral domain D. Our first goal is to study some …

There are many Noetherian-like rings. Among them, we are interested in SFT-rings,
piecewise Noetherian rings, and rings with Noetherian prime spectrum. Some of them are …

Proof. We say that a module RX has an associated prime ideal P if X contains a submodule
isomorphic to RP. To prove the lemma it suffices to show that every nonzero cyclic R-module …

In this paper, we study the closedness such as seminomality and t-closedness, and
Noetherian-like properties such as piecewise Noetherianness and Noetherian spectrum, of …