Freddy van Oystaeyen's Books

Methods of Graded Rings

By: Constantin Nastasescu,Freddy van Oystaeyen

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Methods of Graded Rings

By: Constantin Nastasescu,Freddy van Oystaeyen

The Category of Graded Rings.- The Category of Graded Modules.- Modules over Stronly Graded Rings.- Graded Clifford Theory.- Internal Homogenization.- External Homogenization.- Smash Products.- Localization of Graded Rings.- Application to Gradability.- Appendix A:Some Category Theory.- Appendix B: Dimensions in an abelian Category.- Bibliography.- Index.-

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Page Count

324

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540207465

ISBN 13

9783540207467

Quasi-Hopf Algebras

A Categorical Approach

By: Daniel Bulacu,Stefaan Caenepeel,Florin Panaite,Freddy Van Oystaeyen

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Quasi-Hopf Algebras

A Categorical Approach

By: Daniel Bulacu,Stefaan Caenepeel,Florin Panaite,Freddy Van Oystaeyen

This is the first book to be dedicated entirely to Drinfeld's quasi-Hopf algebras. Ideal for graduate students and researchers in mathematics and mathematical physics, this treatment is largely self-contained, taking the reader from the basics, with complete proofs, to much more advanced topics, with almost complete proofs. Many of the proofs are based on general categorical results; the same approach can then be used in the study of other Hopf-type algebras, for example Turaev or Zunino Hopf algebras, Hom-Hopf algebras, Hopfish algebras, and in general any algebra for which the category of representations is monoidal. Newcomers to the subject will appreciate the detailed introduction to (braided) monoidal categories, (co)algebras and the other tools they will need in this area. More advanced readers will benefit from having recent research gathered in one place, with open questions to inspire their own research.

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Page Count

546

Publisher

Cambridge University Press

Published Date

ISBN 10

1108632653

ISBN 13

9781108632652

Dimensions of Ring Theory

By: C. Nastasescu,Freddy Van Oystaeyen

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Dimensions of Ring Theory

By: C. Nastasescu,Freddy Van Oystaeyen

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of s9phistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

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369

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9400938357

ISBN 13

9789400938359

Abstract Algebra

A Comprehensive Treatment

By: Claudia Menini,Freddy Van Oystaeyen

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Abstract Algebra

A Comprehensive Treatment

By: Claudia Menini,Freddy Van Oystaeyen

In one exceptional volume, Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe, this ambitious, comprehensive book includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory and explains sets, maps, posets, lattices, and other essentials of the algebraic language; Peano's axioms and cardinality; groupoids, semigroups, monoids, groups; and normal subgroups.

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Page Count

784

Publisher

CRC Press

Published Date

ISBN 10

1351991469

ISBN 13

9781351991469

A Primer of Algebraic Geometry

Constructive Computational Methods

By: Huishi Li,Freddy Van Oystaeyen

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A Primer of Algebraic Geometry

Constructive Computational Methods

By: Huishi Li,Freddy Van Oystaeyen

Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more.

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Page Count

393

Publisher

CRC Press

Published Date

ISBN 10

1482270331

ISBN 13

9781482270334

Algebraic Structures as Seen on the Weyl Algebra

By: Freddy Van Oystaeyen

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Algebraic Structures as Seen on the Weyl Algebra

By: Freddy Van Oystaeyen

The book develops some algebraic structure theory based upon properties observed on the Weyl algebra. Filtered and graded rings, finiteness conditions, localizations and rings of fractions, finiteness conditions on rings and modules, homological dimension and the Gelfand-Kirillov dimensions, simple Noetherian algebras and semisimples rings and modules are considered.

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Page Count

164

Publisher

Universidad Almería

Published Date

ISBN 10

841548769X

ISBN 13

9788415487692

Zariskian Filtrations

By: Li Huishi,Freddy Van Oystaeyen

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Zariskian Filtrations

By: Li Huishi,Freddy Van Oystaeyen

In Commutative Algebra certain /-adic filtrations of Noetherian rings, i.e. the so-called Zariski rings, are at the basis of singularity theory. Apart from that it is mainly in the context of Homological Algebra that filtered rings and the associated graded rings are being studied not in the least because of the importance of double complexes and their spectral sequences. Where non-commutative algebra is concerned, applications of the theory of filtrations were mainly restricted to the study of enveloping algebras of Lie algebras and, more extensively even, to the study of rings of differential operators. It is clear that the operation of completion at a filtration has an algebraic genotype but a topological fenotype and it is exactly the symbiosis of Algebra and Topology that works so well in the commutative case, e.g. ideles and adeles in number theory or the theory of local fields, Puisseux series etc, .... . In Non commutative algebra the bridge between Algebra and Analysis is much more narrow and it seems that many analytic techniques of the non-commutative kind are still to be developed. Nevertheless there is the magnificent example of the analytic theory of rings of differential operators and 1J-modules a la Kashiwara-Shapira.

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Page Count

263

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401587590

ISBN 13

9789401587594

Zariskian Filtrations

By: Li Huishi,Freddy Van Oystaeyen

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Zariskian Filtrations

By: Li Huishi,Freddy Van Oystaeyen

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263

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Springer Science & Business Media

Published Date

ISBN 10

9401587590

ISBN 13

9789401587594

Dimensions of Ring Theory

By: C. Nastasescu,Freddy Van Oystaeyen

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Dimensions of Ring Theory

By: C. Nastasescu,Freddy Van Oystaeyen

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Solve jigsaw puzzle

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Page Count

369

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9400938357

ISBN 13

9789400938359

Book's by Freddy van Oystaeyen

Methods of Graded Rings

Methods of Graded Rings

Quasi-Hopf Algebras

Quasi-Hopf Algebras

Dimensions of Ring Theory

Dimensions of Ring Theory

Abstract Algebra

Abstract Algebra

A Primer of Algebraic Geometry

A Primer of Algebraic Geometry

Algebraic Structures as Seen on the Weyl Algebra

Algebraic Structures as Seen on the Weyl Algebra

Zariskian Filtrations

Zariskian Filtrations

Zariskian Filtrations

Zariskian Filtrations

Dimensions of Ring Theory

Dimensions of Ring Theory

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