11 Best Books on Rings and Modules

We have compiled a list of the Best Reference Books on Rings and Modules, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of Rings and Modules Books with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Rings and Modules below.

1."Introduction to Rings and Modules" by C Musili “Introduction to Rings and Modules” Book Review: This book is a comprehensive guide to the fundamentals of ring theory and module theory. The book covers a wide range of topics, starting with basic definitions and properties of rings and modules, and progressing to more advanced concepts such as homomorphisms, free modules, tensor products, and localization. The author provides clear and concise explanations, along with numerous examples and exercises to aid in understanding. This book is an ideal resource for anyone interested in the study of algebraic structures, including students and researchers in mathematics and related fields.
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2."Introductory Lectures on Rings and Modules (London Mathematical Society Student Texts)" by John A Beachy
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3."Rings and Categories of Modules" by F W Anderson and K R Fuller “Rings and Categories of Modules” Book Review: This book is a comprehensive guide to general ring theory, covering topics such as rings, modules, finiteness conditions, Wedderburn-Artin Theorem, and Jacobson radicals. The author also provides clear explanations of many of the classical findings of the artinian rings. With its detailed descriptions and properties of rings and modules, the book is a valuable resource for advanced graduate students.
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4."Lectures on Rings and Modules" by J Lambek “Lectures on Rings and Modules” Book Review: This book gives a comprehensive and understandable account of a significant portion of general ring theory. It explains the basic concepts and characteristics of rings, modules, finiteness conditions, the Wedderburn-Artin Theorem, and Jacobson radicals. The book includes a wide range of well-chosen exercises to help students apply their knowledge. Advanced graduate students can benefit from this book.
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5."Modules and Structures of Rings" by J S Golan “Modules and Structures of Rings” Book Review: This book explains how modules over a ring can help us understand the structure of the ring. It gives important information on current methods used to solve complex classification problems in algebra. This book is aimed at students in their later years of undergraduate studies and graduate students.
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6."Groups, Rings, Modules (Dover Books on Mathematics)" by Maurice Auslander “Groups, Rings, Modules (Dover Books on Mathematics)” Book Review: This book is intended for advanced undergraduate and postgraduate students who have previous knowledge of sets, groups, rings, and vector spaces. It covers sets and maps, monoids and groups, categories and rings in the first part. The second part covers unique factorization domains, general module theory, semisimple rings and modules, and Artinian rings. Part three includes localization and tensor products, principal ideal domains, and applications of fundamental theorems. Algebraic field extensions and Dedekind domains are covered in part four. The book includes exercises at the end of each chapter to help readers practice and reinforce their understanding.
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7."Rings, Modules, and the Total (Frontiers in Mathematics)" by Friedrich Kasch and Adolf Mader “Rings, Modules, and the Total (Frontiers in Mathematics)” Book Review: This book covers the fundamental concepts of ring and module theory and their applications to other areas of mathematics. It starts with an introduction to rings, modules, and the concept of the total. The authors cover topics such as homomorphisms, exact sequences, Noetherian rings, and Hilbert’s syzygy theorem. The book also includes advanced topics such as group rings, local cohomology, and the Auslander-Buchsbaum theorem. The authors use a clear and concise style, and the book includes numerous exercises to reinforce the concepts covered. This book is suitable for advanced undergraduate and graduate students in mathematics. advertisement advertisement
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8."Algebra: Rings, Modules and Categories I (Grundlehren der mathematischen Wissenschaften)" by Carl Faith “Algebra: Rings, Modules and Categories I (Grundlehren der mathematischen Wissenschaften)” Book Review: This book, part of the Grundlehren der mathematischen Wissenschaften series, is aimed at advanced students of algebra. It covers a broad range of topics including rings, modules, categories, and the relationship between them. The book provides clear explanations of key concepts and includes many examples and exercises to aid comprehension. The authors use a formal approach, making use of definitions and theorems to build up the subject from its foundations. This book is recommended for anyone seeking a comprehensive and rigorous treatment of algebra and its applications to rings, modules, and categories.
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9."Graded and Filtered Rings and Modules (Lecture Notes in Mathematics)" by C Nastasescu and F van Oystaeyen
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10."A Course in Ring Theory" by Donald Passman “A Course in Ring Theory” Book Review: This book provides a comprehensive and accessible introduction to the fundamental concepts of ring theory. This book covers topics such as modules, factorization, and polynomial rings, and presents the Wedderburn-Artin theorem in detail. It also offers a wealth of exercises and examples to help readers develop a solid understanding of the subject. This text is suitable for graduate students and researchers in mathematics who want to deepen their knowledge of algebra and its applications.
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11."Ring Theory: Questions and Answers" by George A Duckett
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