Algebras, Rings and Modules, Volume 2: Non-commutative Algebras and Rings

The theory of algebras, rings, and modules is a fundamental domain of modern mathematics, with general algebra poised for major advances in the twenty-first century. This volume is a continuation of the first, focusing on recent results on advanced topics of the structural theory of associative algebras, rings, and modules.

Format: Paperback / softback
Length: 364 pages
Publication date: 31 March 2021
Publisher: Taylor & Francis Ltd

The theory of algebras, rings, and modules is a fundamental domain of modern mathematics that has experienced significant advancements in recent years. General algebra, particularly non-commutative algebra, is poised for major breakthroughs in the twenty-first century, alongside combinatorics, topology, analysis, and probability. This second volume of "Algebras, Rings and Modules: Non-commutative Algebras and Rings" by M. Hazewinkel and N. Gubarenis is a continuation of the first volume, focusing on the most important recent results on advanced topics of the structural theory of associative algebras, rings, and modules.

Algebras, rings, and modules are mathematical structures that represent and manipulate mathematical objects. They provide a framework for understanding and solving problems in various fields, including algebra, geometry, number theory, and physics. Algebras are sets with operations that combine elements to form new elements, while rings are sets with operations that combine elements to form a group. Modules are sets with additional structures that allow for the representation of mathematical objects in different ways.

One of the key challenges in algebra is the study of associative algebras, which are algebras that satisfy certain properties. Associative algebras are used in a wide range of applications, including quantum mechanics, computer science, and engineering. Non-commutative algebra is a branch of algebra that studies algebras that are not commutative, meaning that the order of operations matters. Non-commutative algebra has been used to solve many difficult problems in mathematics, including the classification of finite simple groups and the study of quantum entanglement.

Topology is a branch of mathematics that studies the properties of spaces that are not Euclidean. Topology has been used to solve many problems in physics, including the study of black holes and the theory of relativity. Analysis is a branch of mathematics that studies the properties of functions and sequences. Analysis has been used to solve many problems in mathematics, including the study of differential equations and the theory of probability. Probability is a branch of mathematics that studies the probability of events occurring. Probability has been used to solve many problems in mathematics, including the study of gambling and the design of computer algorithms.

In recent years, there have been significant advances in the theory of algebras, rings, and modules. These advances have been driven by the development of new techniques and the application of these techniques to a wide range of problems. For example, the study of associative algebras has been revolutionized by the development of the theory of category theory, which provides a powerful framework for studying the structure of algebras. The study of non-commutative algebra has been revolutionized by the development of the theory of quantum groups, which provide a new framework for studying the structure of algebras that are not commutative.

In addition to these advances, there have been many other important developments in the theory of algebras, rings, and modules. For example, the study of ring theory has been expanded to include the study of non-commutative rings, which are rings that are not commutative. The study of module theory has been expanded to include the study of non-commutative modules, which are modules that are not commutative.

Despite these advances, there are still many open problems in the theory of algebras, rings, and modules. For example, the classification of finite simple groups is still an open problem, and the study of quantum entanglement is still a very active area of research. In addition, there are many applications of the theory of algebras, rings, and modules that have not yet been fully explored.

In conclusion, the theory of algebras, rings, and modules is a fundamental domain of modern mathematics that has experienced significant advancements in recent years. General algebra, particularly non-commutative algebra, is poised for major breakthroughs in the twenty-first century, alongside combinatorics, topology, analysis, and probability. This second volume of "Algebras, Rings and Modules: Non-commutative Algebras and Rings" by M. Hazewinkel and N. Gubarenis is a continuation of the first volume, focusing on the most important recent results on advanced topics of the structural theory of associative algebras, rings, and modules. While there are still many open problems in the theory of algebras, rings, and modules, there have been many important developments in the field that have had a significant impact on various fields of mathematics.

Weight: 671g
Dimension: 234 x 156 (mm)
ISBN-13: 9780367782504