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Sinopsis
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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Reseña del editor
Excerpt from The Algebraic Theory of Modular Systems
I take this opportunity of thanking the Editors for their accept ance of this tract and the Syndics of the University Press for publishing it.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from The Algebraic Theory of Modular Systems
The present state of our knowledge of the properties of Modular Systems is chiefly due to the fundamental theorems and processes of L. Kronecker, M. Noether, D. Hilbert, and E. Lasker, and above all to J. Konig's profound exposition and numerous extensions of Kronecker's theory (p. xiii). Konig's treatise might be regarded as in some measure complete if it were admitted that a problem is finished with when its solution has been reduced to a finite number of feasible operations. If however the operations are too numerous or too involved to be carried out in practice the solution is only a theoretical one; and its importance then lies not in itself, but in the theorems with which it is associated and to which it leads. Such a theoretical solution must be regarded as a preliminary and not the final stage in the consideration of the problem.
In the following presentment of the subject Section I is devoted to the Resultant, the case of n equations being treated in a parallel manner to that of two equations; Section II contains an account of Kronecker's theory of the Resolvent, following mainly the lines of Konig's exposition; Section III, on general properties, is closely allied to Lasker's memoir and Dedekind's theory of Ideals; and Section IV is an extension of Lasker's results founded on the methods originated by Noether. The additions to the theory consist of one or two isolated theorems (especially 50-53 and 79 and its consequences) and the introduction of the Inverse System in Section IV.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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The Algebraic Theory of Modular Systems (Classic Reprint)
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Paperback. Condición: 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. Nº de ref. del artículo: 9781330386675_0
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The Algebraic Theory of Modular Systems (Classic Reprint)
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