Items related to The Algebraic Theory of Modular Systems (Classic Reprint)
Synopsis
Explore the algebraic foundations behind modular systems and their applications. This concise, theory‑driven work guides you through ideals, modules, and the relationships that bind them, from basic definitions to the structure of complex systems.
This edition presents a clear account of how rank, unmixed versus mixed modules, and prime factors interact within modular systems. It also contrasts Kronecker’s and Dedekind’s approaches, and shows how results can be used to understand linear equations and their solutions in an algebraic setting.
- Understand what it means for a module or ideal to have a certain rank and when it is unmixed.
- Learn how prime factors and divisibility operate in the context of modular systems and algebraic forms.
- See how the theory connects to solving homogeneous linear equations and to the concept of resultants.
- Compare classical viewpoints from Kronecker and Dedekind to modern interpretations.
Ideal for readers who want a rigorous, historically grounded look at the algebra of modular systems and the tools used to factor and solve within that framework.
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Review
"...a landmark in the development of commutative algebra as a separate field..." P. Schenzel, Mathematical Reviews
Book Description
Many of the ideas introduced by Macaulay in this book have developed into central concepts of modern theory. Originally published over 75 years ago, the wealth of thinking expounded here by Macaulay will still be a source of inspiration to all workers in commutative algebra.
"About this title" may belong to another edition of this title.
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The Algebraic Theory of Modular Systems (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book introduces the fundamental theorems and processes of modular systems, as developed by L. Kronecker, M. Noether, D. Hilbert, and E. Lasker. The author presents a thorough exposition of J. KÃ nig's profound extension of Kronecker's theory, laying the groundwork for solving a wide range of problems in algebra. The book offers a detailed examination of the theory of the resultant, resolvent, and general properties of modules. It delves into Lasker's memoir and Dedekinds theory of ideals, extending Lasker's results through Noether's groundbreaking methods. The book's exploration of modular systems is notable for its originality and rigor, providing valuable insights into the nature and significance of these mathematical constructs. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781330386675_0
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