Hilbert Functions of Filtered Modules PDF Download
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Author: Maria Evelina Rossi
Publisher: Springer Science & Business Media
ISBN: 3642142400
Category : Mathematics
Languages : en
Pages : 115
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Book Description
Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are becoming increasingly important also in Computational Algebra. They capture many useful numerical characters associated to a projective variety or to a filtered module over a local ring. Starting from the pioneering work of D.G. Northcott and J. Sally, we aim to gather together in one place many new developments of this theory by using a unifying approach which gives self-contained and easier proofs. The extension of the theory to the case of general filtrations on a module, and its application to the study of certain graded algebras which are not associated to a filtration are two of the main features of the monograph. The material is intended for graduate students and researchers who are interested in Commutative Algebra, in particular in the theory of the Hilbert Functions and related topics.
Author: Maria Evelina Rossi
Publisher: Springer Science & Business Media
ISBN: 3642142400
Category : Mathematics
Languages : en
Pages : 115
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Book Description
Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are becoming increasingly important also in Computational Algebra. They capture many useful numerical characters associated to a projective variety or to a filtered module over a local ring. Starting from the pioneering work of D.G. Northcott and J. Sally, we aim to gather together in one place many new developments of this theory by using a unifying approach which gives self-contained and easier proofs. The extension of the theory to the case of general filtrations on a module, and its application to the study of certain graded algebras which are not associated to a filtration are two of the main features of the monograph. The material is intended for graduate students and researchers who are interested in Commutative Algebra, in particular in the theory of the Hilbert Functions and related topics.
Author: Syed Tariq Rizvi
Publisher: Springer
ISBN: 9811016518
Category : Mathematics
Languages : en
Pages : 431
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Book Description
This book discusses recent developments and the latest research in algebra and related topics. The book allows aspiring researchers to update their understanding of prime rings, generalized derivations, generalized semiderivations, regular semigroups, completely simple semigroups, module hulls, injective hulls, Baer modules, extending modules, local cohomology modules, orthogonal lattices, Banach algebras, multilinear polynomials, fuzzy ideals, Laurent power series, and Hilbert functions. All the contributing authors are leading international academicians and researchers in their respective fields. Most of the papers were presented at the international conference on Algebra and its Applications (ICAA-2014), held at Aligarh Muslim University, India, from December 15–17, 2014. The book also includes papers from mathematicians who couldn't attend the conference. The conference has emerged as a powerful forum offering researchers a venue to meet and discuss advances in algebra and its applications, inspiring further research directions.
Author: Alexander V. Mikhalev
Publisher: Springer Science & Business Media
ISBN: 9401712573
Category : Mathematics
Languages : en
Pages : 434
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Book Description
The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known. A similar role in differential algebra is played by the differential dimension polynomials. The notion of differential dimension polynomial was introduced by E. Kolchin in 1964 [KoI64]' but the problems and ideas that had led to this notion (and that are reflected in this book) have essentially more long history. Actually, one can say that the differential dimension polynomial describes in exact terms the freedom degree of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations. The first attempts of such description were made at the end of 19th century by Jacobi [Ja890] who estimated the number of algebraically independent constants in the general solution of a system of linear ordinary differential equations. Later on, Jacobi's results were extended to some cases of nonlinear systems, but in general case the problem of such estimation (that is known as the problem of Jacobi's bound) remains open. There are some generalization of the problem of Jacobi's bound to the partial differential equations, but the results in this area are just appearing. At the beginning of the 20th century algebraic methods in the theory of differen tial equations were actively developed by F. Riquier [RiqlO] and M.
Author: Alberto Corso
Publisher: American Mathematical Soc.
ISBN: 082184959X
Category : Mathematics
Languages : en
Pages : 233
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Book Description
This volume contains papers based on presentations given at the Pan-American Advanced Studies Institute (PASI) on commutative algebra and its connections to geometry, which was held August 3-14, 2009, at the Universidade Federal de Pernambuco in Olinda, Brazil. The main goal of the program was to detail recent developments in commutative algebra and interactions with such areas as algebraic geometry, combinatorics and computer algebra. The articles in this volume concentrate on topics central to modern commutative algebra: the homological conjectures, problems in positive and mixed characteristic, tight closure and its interaction with birational geometry, integral dependence and blowup algebras, equisingularity theory, Hilbert functions and multiplicities, combinatorial commutative algebra, Grobner bases and computational algebra.
Author: Jun-ichi Igusa
Publisher: American Mathematical Soc.
ISBN: 0821829076
Category : Mathematics
Languages : en
Pages : 246
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Book Description
This book is an introductory presentation to the theory of local zeta functions. Viewed as distributions, and mostly in the archimedean case, local zeta functions are also called complex powers. The volume contains major results on analytic and algebraic properties of complex powers by Atiyah, Bernstein, I. M. Gelfand, S. I. Gelfand, and Sato. Chapters devoted to $p$-adic local zeta functions present Serre's structure theorem, a rationality theorem, and many examples found by the author. The presentation concludes with theorems by Denef and Meuser. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.
Author: Irena Peeva
Publisher: Springer Science & Business Media
ISBN: 1461452929
Category : Mathematics
Languages : en
Pages : 705
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Book Description
This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.
Author: Aldo Conca
Publisher: Springer
ISBN: 3319619438
Category : Mathematics
Languages : en
Pages : 265
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Book Description
This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting “Homological and Computational Methods in Commutative Algebra” held in Cortona (Italy) from May 30 to June 3, 2016 . The conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th birthday. In particular, the topics of this book strongly reflect the variety of Winfried Bruns’ research interests and his great impact on commutative algebra as well as its applications to related fields. The authors discuss recent and relevant developments in algebraic geometry, commutative algebra, computational algebra, discrete geometry and homological algebra. The book offers a unique resource, both for young and more experienced researchers seeking comprehensive overviews and extensive bibliographic references.
Author: Alexander Levin
Publisher: Springer Science & Business Media
ISBN: 1402069472
Category : Mathematics
Languages : en
Pages : 528
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Book Description
Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields. The first stage of this development of the theory is associated with its founder, J.F. Ritt (1893-1951), and R. Cohn, whose book Difference Algebra (1965) remained the only fundamental monograph on the subject for many years. Nowadays, difference algebra has overgrown the frame of the theory of ordinary algebraic difference equations and appears as a rich theory with applications to the study of equations in finite differences, functional equations, differential equations with delay, algebraic structures with operators, group and semigroup rings. The monograph is intended for graduate students and researchers in difference and differential algebra, commutative algebra, ring theory, and algebraic geometry. The book is self-contained; it requires no prerequisites other than the knowledge of basic algebraic concepts and a mathematical maturity of an advanced undergraduate.
Author: M. Hazewinkel
Publisher: Elsevier
ISBN: 0080462499
Category : Mathematics
Languages : en
Pages : 543
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Book Description
Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.- Thorough and practical source for information- Provides in-depth coverage of new topics in algebra- Includes references to relevant articles, books and lecture notes
Author: Nguyen Tu CUONG
Publisher: Springer
ISBN: 331975565X
Category : Mathematics
Languages : en
Pages : 265
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Book Description
This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. Aimed at researchers and graduate students with an advanced background in algebra, these lectures were given during the Commutative Algebra program held at the Vietnam Institute of Advanced Study in Mathematics in the winter semester 2013 -2014. The first lecture is on Weyl algebras (certain rings of differential operators) and their D-modules, relating non-commutative and commutative algebra to algebraic geometry and analysis in a very appealing way. The second lecture concerns local systems, their homological origin, and applications to the classification of Artinian Gorenstein rings and the computation of their invariants. The third lecture is on the representation type of projective varieties and the classification of arithmetically Cohen -Macaulay bundles and Ulrich bundles. Related topics such as moduli spaces of sheaves, liaison theory, minimal resolutions, and Hilbert schemes of points are also covered. The last lecture addresses a classical problem: how many equations are needed to define an algebraic variety set-theoretically? It systematically covers (and improves) recent results for the case of toric varieties.
