Lattice-ordered Rings and Modules

Lattice-ordered Rings and Modules
Author: Stuart A. Steinberg
Publisher: Springer Science & Business Media
Total Pages: 639
Release: 2009-11-19
Genre: Mathematics
ISBN: 1441917217

This book provides an exposition of the algebraic aspects of the theory of lattice-ordered rings and lattice-ordered modules. All of the background material on rings, modules, and lattice-ordered groups necessary to make the work self-contained and accessible to a variety of readers is included. Filling a gap in the literature, Lattice-Ordered Rings and Modules may be used as a textbook or for self-study by graduate students and researchers studying lattice-ordered rings and lattice-ordered modules. Steinberg presents the material through 800+ extensive examples of varying levels of difficulty along with numerous exercises at the end of each section. Key topics include: lattice-ordered groups, rings, and fields; archimedean $l$-groups; f-rings and larger varieties of $l$-rings; the category of f-modules; various commutativity results.

Lecture Notes On Algebraic Structure Of Lattice-ordered Rings

Lecture Notes On Algebraic Structure Of Lattice-ordered Rings
Author: Jingjing Ma
Publisher: World Scientific
Total Pages: 258
Release: 2014-03-14
Genre: Mathematics
ISBN: 981457144X

Algebraic Structure of Lattice-Ordered Rings presents an introduction to the theory of lattice-ordered rings and some new developments in this area in the last 10-15 years. It aims to provide the reader with a good foundation in the subject, as well as some new research ideas and topic in the field.This book may be used as a textbook for graduate and advanced undergraduate students who have completed an abstract algebra course including general topics on group, ring, module, and field. It is also suitable for readers with some background in abstract algebra and are interested in lattice-ordered rings to use as a self-study book.The book is largely self-contained, except in a few places, and contains about 200 exercises to assist the reader to better understand the text and practice some ideas.

Partially Ordered Algebraic Systems

Partially Ordered Algebraic Systems
Author: Laszlo Fuchs
Publisher: Courier Corporation
Total Pages: 242
Release: 2014-03-05
Genre: Mathematics
ISBN: 0486173607

This monograph by a distinguished mathematician constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The high-level, self-contained treatment features numerous problems. 1963 edition.

Algebras, Rings and Modules

Algebras, Rings and Modules
Author: Michiel Hazewinkel
Publisher: CRC Press
Total Pages: 384
Release: 2016-04-05
Genre: Mathematics
ISBN: 1482245051

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth centu

Technical Report

Technical Report
Author: Indian Institute of Technology Kānpur. Dept. of Mathematics
Publisher:
Total Pages: 680
Release: 1970
Genre: Mathematics
ISBN:

Nearrings, Nearfields And Related Topics

Nearrings, Nearfields And Related Topics
Author: Kuncham Syam Prasad
Publisher: World Scientific
Total Pages: 324
Release: 2016-11-28
Genre: Mathematics
ISBN: 981320737X

Recent developments in various algebraic structures and the applications of those in different areas play an important role in Science and Technology. One of the best tools to study the non-linear algebraic systems is the theory of Near-rings.The forward note by G

Introduction to the Theory of Abstract Algebras

Introduction to the Theory of Abstract Algebras
Author: Richard S Pierce
Publisher: Courier Corporation
Total Pages: 162
Release: 2015-01-21
Genre: Mathematics
ISBN: 0486789985

"Suitable for introductory graduate-level courses and independent study, this text presents the basic definitions of the theory of abstract algebra. Following introductory material, each of four chapters focuses on a major theme of universal algebra: subdirect decompositions, direct decompositions, free algebras, and varieties of algebra. Problems and a bibliography supplement the text. "--

Selected Papers on Algebra and Topology by Garrett Birkhoff

Selected Papers on Algebra and Topology by Garrett Birkhoff
Author: J.S. Oliveira
Publisher: Springer Science & Business Media
Total Pages: 648
Release: 1987-01-01
Genre: Science
ISBN: 9780817631147

The present volume of reprints are what I consider to be my most interesting and influential papers on algebra and topology. To tie them together, and to place them in context, I have supplemented them by a series of brief essays sketching their historieal background (as I see it). In addition to these I have listed some subsequent papers by others which have further developed some of my key ideas. The papers on universal algebra, lattice theory, and general topology collected in the present volume concern ideas which have become familiar to all working mathematicians. It may be helpful to make them readily accessible in one volume. I have tried in the introduction to each part to state the most significant features of ea ch paper reprinted there, and to indieate later developments. The background that shaped and stimulated my early work on universal algebra, lattice theory, and topology may be of some interest. As a Harvard undergraduate in 1928-32, I was encouraged to do independent reading and to write an original thesis. My tutorial reading included de la Vallee-Poussin's beautiful Cours d'Analyse Infinitesimale, Hausdorff's Grundzüge der Mengenlehre, and Frechet's Espaces Abstraits. In addition, I discovered Caratheodory's 1912 paper "Vber das lineare Mass von Punktmengen" and Hausdorff's 1919 paper on "Dimension und Ausseres Mass," and derived much inspiration from them. A fragment of my thesis, analyzing axiom systems for separable metrizable spaces, was later published [2]. * This background led to the work summarized in Part IV.