S. K. Jain

A. Leroy

This volume contains the proceedings of the Virtual Conference on Noncommutative Rings and their Applications VII, in honor of Tariq Rizvi, held from July 5–7, 2021, and the Virtual Conference on Quadratic Forms, Rings and Codes, held on July 8, 2021, both of which were hosted by the Université d'Artois, Lens, France. The articles cover topics in commutative and noncommutative algebra and applications to coding theory. In some papers, applications of Frobenius rings, the skew group rings, and iterated Ore extensions to coding theory are discussed. Other papers discuss classical topics, such as Utumi rings, Baer rings, nil and nilpotent algebras, and Brauer groups. Still other articles are devoted to various aspects of the elementwise study for rings and modules. Lastly, this volume includes papers dealing with questions in homological algebra and lattice theory. The articles in this volume show the vivacity of the research of noncommutative rings and its influence on other subjects.

Algebra and Coding Theory

Askar A. Tuganbaev

Ashish K. Srivastava

This unique and comprehensive volume provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property. The finiteness conditions and homological properties are closely interrelated in the sense that either hypothesis induces the other in some form. This is the first book to bring all of this important material on the subject together. Over the last 25 years or more numerous mathematicians have investigated rings whose factor rings or factor modules have a finiteness condition or a homological property. They made important contributions leading to new directions and questions, which are listed at the end of each chapter for the benefit of future researchers. There is a wealth of material on the topic which is combined in this book, it contains more than 200 references and is not claimed to be exhaustive. This book will appeal to graduate students, researchers, and professionals in algebra with a knowledge of basic noncommutative ring theory, as well as module theory and homological algebra, equivalent to a one-year graduate course in the theory of rings and modules.

Cyclic Modules and the Structure of Rings

P. B. Bhattacharya

S. R. Nagpaul

This book provides a complete abstract algebra course, enabling instructors to select the topics for use in individual classes.

Basic Abstract Algebra

Sanyog Rawat

Anirban Bandyopadhyay

Kanad Ray

S. N. Sharan

Sumit Srivastava

This book discusses the revolution of cycles and rhythms that is expected to take place in different branches of science and engineering in the 21st century, with a focus on communication and information processing. It presents high-quality papers in vibration sciences, rhythms and oscillations, neurosciences, mathematical sciences, and communication. It includes major topics in engineering and structural mechanics, computer sciences, biophysics and biomathematics, as well as other related fields. Offering valuable insights, it also inspires researchers to work in these fields. The papers included in this book were presented at the 1st International Conference on Engineering Vibration, Communication and Information Processing (ICoEVCI-2018), India.

ICoEVCI 2018, India

Engineering Vibration, Communication and Information Processing

This book represents a complete course in abstract algebra, providing instructors with flexibility in the selection of topics to be taught in individual classes. All the topics presented are discussed in a direct and detailed manner. Throughout the text, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. The book contains many examples fully worked out and a variety of problems for practice and challenge. Solutions to the odd-numbered problems are provided at the end of the book. This new edition contains an introduction to lattices, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Lasker–Noether theorem. In addition, there are over 100 new problems and examples, particularly aimed at relating abstract concepts to concrete situations.

S. K. Jain

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