Non Commutative Localization In Algebra And Topology

Author : Andrew Ranicki
Publisher : Cambridge University Press
Page : 332 pages
File Size : 43,6 Mb
Release : 2006-02-09
Category : Mathematics
ISBN : 052168160X

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Noncommutative Localization in Algebra and Topology by Andrew Ranicki Pdf

Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.

Author : Department of Mathematics and Statistics Andrew Ranicki
Publisher : Unknown
Page : 329 pages
File Size : 40,5 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362822

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Non-Commutative Localization in Algebra and Topology by Department of Mathematics and Statistics Andrew Ranicki Pdf

An introduction to noncommutative localization and an account of the state of the art suitable for researchers and graduate students.

Author : F.M.J. van Oystaeyen,A.H.M.J. Verschoren
Publisher : Springer
Page : 408 pages
File Size : 48,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540386018

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Non-commutative Algebraic Geometry by F.M.J. van Oystaeyen,A.H.M.J. Verschoren Pdf

Author : J. P. May,K. Ponto
Publisher : University of Chicago Press
Page : 544 pages
File Size : 49,8 Mb
Release : 2012-02
Category : Mathematics
ISBN : 9780226511788

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More Concise Algebraic Topology by J. P. May,K. Ponto Pdf

With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras. The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.

Author : Gwyn Bellamy,Daniel Rogalski,Travis Schedler,J. Toby Stafford,Michael Wemyss
Publisher : Cambridge University Press
Page : 367 pages
File Size : 55,8 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9781107129542

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Noncommutative Algebraic Geometry by Gwyn Bellamy,Daniel Rogalski,Travis Schedler,J. Toby Stafford,Michael Wemyss Pdf

This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.

Author : Igor V. Nikolaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 400 pages
File Size : 46,7 Mb
Release : 2022-07-18
Category : Mathematics
ISBN : 9783110788709

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Noncommutative Geometry by Igor V. Nikolaev Pdf

Noncommutative geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. This book covers the key concepts of noncommutative geometry and its applications in topology, algebraic geometry, and number theory. Our presentation is accessible to the graduate students as well as nonexperts in the field. The second edition includes two new chapters on arithmetic topology and quantum arithmetic.

Author : Freddy Van Oystaeyen
Publisher : CRC Press
Page : 302 pages
File Size : 41,7 Mb
Release : 2000-06-06
Category : Mathematics
ISBN : 9781482270525

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Algebraic Geometry for Associative Algebras by Freddy Van Oystaeyen Pdf

This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theor

Author : Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 52,5 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 3540203575

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Noncommutative Geometry by Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts Pdf

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Author : Jara Pascual,Conchi Vidal,A Verschoren
Publisher : CRC Press
Page : 260 pages
File Size : 40,7 Mb
Release : 1995-11-30
Category : Mathematics
ISBN : 0582273722

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Localization and Sheaves by Jara Pascual,Conchi Vidal,A Verschoren Pdf

This book completely solves the problem of representing rings (and modules over them), which are locally noetherian over subsets of their prime spectrum by structure sheaves over this subset. In order to realise this, one has to develop the necessary localization theory as well as to study local equivalents of familiar concepts like the Artin-Rees property, Ore sets and the second layer condition. The first part of the book is introductory and self-contained, and might serve as a starting course (at graduate level) on localization theory within Grothendieck categories. The second part is more specialised and provides the basic machinery needed to effectively these structure sheaves, as well as to study their functorial behaviour. In this way, the book should be viewed as a first introduction to what should be called relative noncommutative algebraic geometry.

Author : Jose M. Gracia-Bondia,Joseph C. Varilly,Hector Figueroa
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 40,6 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461200055

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Elements of Noncommutative Geometry by Jose M. Gracia-Bondia,Joseph C. Varilly,Hector Figueroa Pdf

Author : Paul Frank Baum,Guillermo Cortiñas,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën
Publisher : Springer
Page : 308 pages
File Size : 52,5 Mb
Release : 2010-10-28
Category : Mathematics
ISBN : 9783642157080

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Topics in Algebraic and Topological K-Theory by Paul Frank Baum,Guillermo Cortiñas,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën Pdf

This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.

Author : Masoud Khalkhali
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 49,9 Mb
Release : 2011
Category : Algebra, Homological
ISBN : 9780821848494

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Perspectives on Noncommutative Geometry by Masoud Khalkhali Pdf

This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008. Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture. Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples. Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume. This book is intended for graduate students and researchers in both mathematics and theoretical physics who are interested in noncommutative geometry and its applications.

Author : Surender Kumar Jain,S. Parvathi,Dinesh Khurana
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 54,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821842850

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Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications by Surender Kumar Jain,S. Parvathi,Dinesh Khurana Pdf

Articles in this volume are based on talks given at the International Conference on Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications. The conference provided researchers in mathematics with the opportunity to discuss new developments in these rapidly growing fields. This book contains several excellent articles, both expository and original, with new and significant results. It is suitable for graduate students and researchers interested in Ring Theory,Diagram Algebras and related topics.

Author : Jonathan S. Golan
Publisher : CRC Press
Page : 352 pages
File Size : 53,7 Mb
Release : 1975-01-01
Category : Mathematics
ISBN : 0824761987

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Localization of Noncommutative Rings by Jonathan S. Golan Pdf

Author : Christian Ausoni,Kathryn Hess,Jérôme Scherer
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 49,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821848395

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Alpine Perspectives on Algebraic Topology by Christian Ausoni,Kathryn Hess,Jérôme Scherer Pdf

Contains the proceedings of the Third Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, on August 18-24, 2008. This title includes research papers on stable homotopy theory, the theory of operads, localization and algebraic K-theory, as well as survey papers on the Witten genus and localization techniques.