Rings

This book deals with a new class of materials, quantum rings. Innovative recent advances in experimental and theoretical physics of quantum rings are based on the most advanced state-of-the-art fabrication and characterization techniques as well as theoretical methods. The experimental efforts allow to obtain a new class of semiconductor quantum rings formed by capping self-organized quantum dots grown by molecular beam epitaxy. Novel optical and magnetic properties of quantum rings are associated with non-trivial topologies at the nanoscale.

Classically Semisimple Rings is a textbook on rings, modules and categories, aimed at advanced undergraduate and beginning graduate students.

This book contains select papers on rings, monoids and module theory which are presented at the 3rd International Conference on Mathematics and Statistics (AUS-ICMS 2020) held at the American University of Sharjah, United Arab Emirates, from 6–9 February 2020. This conference was held in honour of the work of the distinguished algebraist Daniel D. Anderson.

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.

Physics of Planetary Rings describes striking structures of the planetary rings of Saturn, Uranus, Jupiter, and Neptune: Narrow ringlets, spiral waves, and a chain of clumps. The author has contributed essential ideas to the full understanding of planetary rings via the stability analysis of dynamical systems. The combination of a high-quality description, the set of interesting illustrations, as well as the fascinating and natural presentation will make this book of considerable interest to astronomers, physicists, and mathematicians as well as students. There is no competing text for this book so far.

This Problem Book offers a compendium of 639 exercises of varying degrees of difficulty in the subject of modules and rings at the graduate level. The material covered includes projective, injective, and flat modules, homological and uniform dimensions, noncommutative localizations and Goldie’s theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, as well as Morita’s classical theory of category dualities and equivalences.

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time.

This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account on the subject.