Foundations of module and ring theory

  title={Foundations of module and ring theory},
  author={Robert Wisbauer},
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 stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and… 
Topics in torsion theory
The purpose of this thesis is to generalize to the torsion-theoretic setting various concepts and results from the theory of rings and modules. In order to accomplish this we begin with some
A generalization of supplemented modules
Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a class of modules which is an analogous of -supplemented modules defined by Kosan. The module M is called
A generalization of the classical Krull dimension for modules
High and Low Formulas in Modules
A partition of the set of unary pp formulas into four regions is presented, which has a bearing on various structural properties of modules. The machinery developed allows for applications to IF,
Pure-projective modules and positive constructibility
It is proved here, Theorem 3.1, that the pure-projective modules are exactly the positively constructible modules.
Distributive Invariant Centrally Essential Rings
. In recent years, centrally essential rings have been intensively studied in ring theory. In particular, they find applications in homological algebra, group rings, and the structural theory of
The injective spectrum of a right noetherian ring
On topological lattices and their applications to module theory
Yassemi’s “second submodules” are dualized and properties of its spectrum are studied. This is done by moving the ring theoretical setting to a lattice theoretical one and by introducing the notion
Completely irreducible meet decompositions in lattices, with applications to Grothendieck categories and torsion theories (II)
The aim of this paper, consisting of two parts, is to investigate decompositions of elements in upper continuous modular lattices as intersections of (completely) irreducible elements. Thus, we


Rings and Categories of Modules
This book is intended to provide a self-contained account of much of the theory of rings and modules. The theme of the text throughout is the relationship between the one-sided ideal structure a ring
Elementary Equivalence of ∑-Injective Modules
Let R be a ring with 1 and consider the problem of assigning numerical invariants to right K-modules so that two such modules are elementarily equivalent if and only if they have the same invariants.
Morita equivalence for rings withot identity
In the paper [1] Abrams made a first step in extending the theory of Morita equivalence to rings without identity. He considered rings in which a set of commuting idempotents is given such that every
A characterization of artinian rings
Throughout this paper we consider associative rings with identity and assume that all modules are unitary. As is well known, cyclic modules play an important role in ring theory. Many nice properties
On the Structure of Linearly Compact Rings and Their Dualities
In this work we study (left) linearly compact (i.e.) rings giving contributions in the following three directions. A theorem of representation of any 1.e. ring as the endo-morphism ring of a
An Introduction to Homological Algebra
An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext
A characterization of perfect rings
J. P. Jans has shown that if a ring R is right perfect, then a certain torsion in the category Mod R of left ϋί-modules is closed under taking direct products. Extending his method, J. S. Alin and E.