Module Theory: An Approach to Linear Algebra 2nd Edition by T. S. Blyth (PDF)

Description

This textbook provides a self-contained course on the basic properties of modules and their importance in the theory of linear algebra. The first 11 chapters introduce the central results and applications of the theory of modules. Subsequent chapters deal with advanced linear algebra,including multilinear and tensor algebra, and explore such topics as the exterior product approach to the determinants of matrices, a module-theoretic approach to the structure of finitely generated Abelian groups, canonical forms, and normal transformations. Suitable for undergraduate courses, thetext now includes a proof of the celebrated Wedderburn-Artin theorem which determines the structure of simple Artinian rings.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book claims to be self-contained. The preface describes the target audience ass “first year honors students” but the very first section of the text starts from development based on polynomial rings and modules. Obviously, the author has an exaggerated opinion of first year students (does he mean first year graduate students?) But overall, assuming such knowledge, the book is concise and well developed and a pleasure to read

⭐Being an introduction to so many branches of mathematics and still self contained in the development of a specific theory, I think this book is a must for anyone who wants to get at least a glimpse of what lies beyond the curtains of real mathematics. I studied the book as an undergraduate, and the subject was hard to me, which made it all the more fun. I have pursued my graduate work in physics and although not directly helpful yet, the introduction to commutative diagrams, homological algebra, the abstract approach to products and coproducts and many other advanced subjects of mathematics has really been a wonderful intellectual challenge.

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