The Algebraic Theory of Modular Systems
Author | : Francis Sowerby Macaulay |
Publisher | : |
Total Pages | : 132 |
Release | : 1916 |
Genre | : Elimination |
ISBN | : |
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Author | : Francis Sowerby Macaulay |
Publisher | : |
Total Pages | : 132 |
Release | : 1916 |
Genre | : Elimination |
ISBN | : |
Author | : F S Macaulay |
Publisher | : Legare Street Press |
Total Pages | : 0 |
Release | : 2023-07-18 |
Genre | : |
ISBN | : 9781019399620 |
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.
Author | : FRANCIS SOWERBY. MACAULAY |
Publisher | : |
Total Pages | : 0 |
Release | : 2019 |
Genre | : |
ISBN | : 9781033349946 |
Author | : American Mathematical Society |
Publisher | : |
Total Pages | : 562 |
Release | : 1907 |
Genre | : Mathematics |
ISBN | : |
Author | : Teo Mora |
Publisher | : Cambridge University Press |
Total Pages | : 833 |
Release | : 2016-04-01 |
Genre | : Mathematics |
ISBN | : 1316381382 |
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.
Author | : David Eisenbud |
Publisher | : Springer Science & Business Media |
Total Pages | : 822 |
Release | : 1995-03-30 |
Genre | : Mathematics |
ISBN | : 9780387942698 |
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Author | : Wladyslaw Narkiewicz |
Publisher | : Springer Science & Business Media |
Total Pages | : 712 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662070014 |
This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Author | : Karin Gatermann |
Publisher | : Springer |
Total Pages | : 163 |
Release | : 2007-05-06 |
Genre | : Mathematics |
ISBN | : 3540465197 |
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.
Author | : Edward Frenkel |
Publisher | : American Mathematical Soc. |
Total Pages | : 418 |
Release | : 2004-08-25 |
Genre | : Mathematics |
ISBN | : 0821836749 |
Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.