There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star …

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 …

Let R be a commutative ring with identity and let 𝒬 be the set of finitely generated
semiregular ideals of R. A 𝒬-torsion-free R-module M is called a Lucas module if Ext R 1 …

A finite fraction over a commutative ring R is a rational function of the form f=(an X n+…+ a
0)(bn X n+…+ b 0) for which fb i= ai and a (X), b (X)∈ R [X]. The collection of all such finite …

All rings considered in this survey are commutative with identity. Let A be a subring of a ring
B (with the same 1) and let n⩽ 1 be an integer. We say that A is n-root closed in B if bn ϵ A …

This paper deals with extending the notions of Krull domains and PvMDs to rings with zero
divisors. Two of the problems to be addressed involve characterizing when the Nagata ring …

Publisher Summary This chapter reviews the results and methods in linear algebra over
commutative rings. This theory is formed by systems of linear equations and linear …

In this article, a new semistar operation, called the q-operation, on a commutative ring R is
introduced in terms of the ring Q 0 (R) of finite fractions. It is defined as the map q: F q (R)→ F …

Elliott and Lucas each introduced “Q 0” variants of Dedekind rings, Krull rings, and Prüfer (v-
multiplication) rings. These rings are defined analogously to their classical counterparts, but …

This paper is devoted to the study of t-closed rings. Let us begin by giving some informations
about the historical development of t-closedness. The importance of seminormal rings and …