Download or read book The Algebraic Theory of Modular Systems written by Francis Sowerby Macaulay and published by . This book was released on 1916 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Algebraic Theory of Modular Systems written by F S Macaulay and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work by Francis S. Macaulay is a comprehensive exploration of the algebraic theory of modular systems. The book covers a range of topics, including the theory of groups, rings, fields, and modules, and provides a detailed analysis of the properties of modular systems. It is an essential resource for anyone interested in abstract algebra or mathematics in general. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book ALGEBRAIC THEORY OF MODULAR SYSTEMS written by FRANCIS SOWERBY. MACAULAY and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Algebraic Theory of Modular Systems written by Francis Sowerby Macaulay and published by Forgotten Books. This book was released on 2015-06-25 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Algebraic Theory of Modular Systems written by Francis Sowerby Macaulay and published by . This book was released on 1992 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Algebraic Theory of Modular Systems written by F. Macaulay and published by Createspace Independent Publishing Platform. This book was released on 2017-09-18 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface. 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 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. The subject is full of pitfalls. I have pointed out some mistakes made by others, but have no doubt that I have made new ones. It may be expected that any errors will be discovered and eliminated in due course, since proofs or references are given for all major and most minor statements. I take this opportunity of thanking the Editors for their acceptance of this tract and the Syndics of the University Press for publishing it.
Download or read book The Algebraic Theory of Modular Systems Moderne Algebraische Geometrie written by Francis Sowerby Macaulay and published by . This book was released on 1916 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Algebraic Theory of Modular Systems Primary Source Edition written by F. S. 1862-1937 Macaulay and published by Nabu Press. This book was released on 2014-02 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
Download or read book The Algebraic Theory of Module Systems written by F S Macaulay and published by Independently Published. This book was released on 2019-06-27 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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. The subject is full of pitfalls. I have pointed out some mistakes made by others, but have no doubt that I have made new ones. It may be expected that any errors will be discovered and eliminated in due course, since proofs or references are given for all major and most minor statements. I take this opportunity of thanking the Editors for their acceptance of this tract and the Syndics of the University Press for publishing it.
Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1907 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin new Series of the American Mathematical Society written by and published by . This book was released on 1907 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Theory for Multivariable Linear Systems written by Blomberg and published by Academic Press. This book was released on 1983-06-14 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Theory for Multivariable Linear Systems
Download or read book Solving Polynomial Equation Systems IV Volume 4 Buchberger Theory and Beyond written by Teo Mora and published by Cambridge University Press. This book was released on 2016-04-01 with total page 833 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Download or read book Modular Invariant Theory written by H.E.A. Eddy Campbell and published by Springer Science & Business Media. This book was released on 2011-01-12 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers—an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.
Download or read book Solving Polynomial Equation Systems III Volume 3 Algebraic Solving written by Teo Mora and published by Cambridge University Press. This book was released on 2015-08-07 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Gröbner bases, which allow one to manipulate the roots of the equation rather than just compute them. The book begins with the 'standard' solutions (Gianni–Kalkbrener Theorem, Stetter Algorithm, Cardinal–Mourrain result) and then moves on to more innovative methods (Lazard triangular sets, Rouillier's Rational Univariate Representation, the TERA Kronecker package). The author also looks at classical results, such as Macaulay's Matrix, and provides a historical survey of elimination, from Bézout to Cayley. This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Download or read book Computer Algebra Methods for Equivariant Dynamical Systems written by Karin Gatermann and published by Springer. This book was released on 2007-05-06 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.
Download or read book Solving Polynomial Equation Systems written by Teo Mora and published by Cambridge University Press. This book was released on 2003 with total page 833 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers extensions of Buchberger's Theory and Algorithm, and promising recent alternatives to Gröbner bases.
