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Author : R.M. Fossum,P.A. Griffith,I. Reiten
Publisher : Springer
Page : 133 pages
File Size : 46,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540374879
Author : R. M. Fossum,P. A. Griffith,I. Reiten
Publisher : Unknown
Page : 140 pages
File Size : 53,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662208172
Author : Robert M. Fossum
Publisher : Unknown
Page : 381 pages
File Size : 47,6 Mb
Release : 1975
Category : Abelian categories
ISBN : 0387071598
Author : Apostolos Beligiannis,Idun Reiten
Publisher : American Mathematical Soc.
Page : 207 pages
File Size : 49,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821839966
In this paper the authors investigate homological and homotopical aspects of a concept of torsion which is general enough to cover torsion and cotorsion pairs in abelian categories, $t$-structures and recollements in triangulated categories, and torsion pairs in stable categories. The proper conceptual framework for this study is the general setting of pretriangulated categories, an omnipresent class of additive categories which includes abelian, triangulated, stable, and more generally (homotopy categories of) closed model categories in the sense of Quillen, as special cases. The main focus of their study is on the investigation of the strong connections and the interplay between (co)torsion pairs and tilting theory in abelian, triangulated and stable categories on one hand, and universal cohomology theories induced by torsion pairs on the other hand. These new universal cohomology theories provide a natural generalization of the Tate-Vogel (co)homology theory. The authors also study the connections between torsion theories and closed model structures, which allow them to classify all cotorsion pairs in an abelian category and all torsion pairs in a stable category, in homotopical terms. For instance they obtain a classification of (co)tilting modules along these lines. Finally they give torsion theoretic applications to the structure of Gorenstein and Cohen-Macaulay categories, which provide a natural generalization of Gorenstein and Cohen-Macaulay rings.
Author : Dieter Happel,Idun Reiten,Sverre O. Smalø
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 54,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804445
In this book, the authors generalize with respect to a tilting module of projective dimension at most one for an artin algebra to tilting with respect to a torsion pair in an abelian category. A general theory is developed for such tilting and the reader is led to a generalization for tilted algebras which the authors call ``quasitilted algebras''. This class also contains the canonical algebras, and the authors show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. The authors also give other characterizations of quasitilted algebras and give methods for constructing such algebras. In particular, they investigate when one-point extensions of hereditary algebras are quasitilted.
Author : Hvedri Inassaridze
Publisher : Springer
Page : 324 pages
File Size : 45,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540471622
Author : Pat Goeters,Overtoun M.G. Jenda
Publisher : CRC Press
Page : 354 pages
File Size : 46,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781420010763
About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the par
Author : P.I. Johnstone,R. Pare,R.D. Rosebrugh,D. Schumacher,R.J. Wood,G.C. Wraith
Publisher : Springer
Page : 271 pages
File Size : 45,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540357629
Author : Nicolae Popescu
Publisher : Unknown
Page : 488 pages
File Size : 50,7 Mb
Release : 1973
Category : Mathematics
ISBN : UOM:39015038950625
Author : M. Hazewinkel
Publisher : Springer
Page : 927 pages
File Size : 43,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781489937971
Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 517 pages
File Size : 45,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400960008
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathematics. It is a translation with updates and editorial comments of the Soviet Mathematical En cyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977 - 1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivision has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathe matics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, engineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Author : Ragnar-Olaf Buchweitz
Publisher : American Mathematical Society
Page : 175 pages
File Size : 50,7 Mb
Release : 2021-12-16
Category : Mathematics
ISBN : 9781470453404
This book is a lightly edited version of the unpublished manuscript Maximal Cohen–Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen–Macaulay modules over (not necessarily commutative) Gorenstein rings. The main result is that the stable category of maximal Cohen–Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. This assimilates and significantly extends earlier work of Eisenbud on hypersurface singularities. There is also an extensive discussion of duality phenomena in stable derived categories, extending Tate duality on cohomology of finite groups. Another noteworthy aspect is an extension of the classical BGG correspondence to super-algebras. There are numerous examples that illustrate these ideas. The text includes a survey of developments subsequent to, and connected with, Buchweitz's manuscript.
Author : Freddy Van Oystaeyen
Publisher : CRC Press
Page : 302 pages
File Size : 50,5 Mb
Release : 2000-06-06
Category : Mathematics
ISBN : 9781482270525
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 : Klaus W. Roggenkamp,Mirela Stefanescu
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 47,5 Mb
Release : 2001-08-31
Category : Mathematics
ISBN : 0792371135
Over the last three decades representation theory of groups, Lie algebras and associative algebras has undergone a rapid development through the powerful tool of almost split sequences and the Auslander-Reiten quiver. Further insight into the homology of finite groups has illuminated their representation theory. The study of Hopf algebras and non-commutative geometry is another new branch of representation theory which pushes the classical theory further. All this can only be seen in connection with an understanding of the structure of special classes of rings. The aim of this book is to introduce the reader to some modern developments in: Lie algebras, quantum groups, Hopf algebras and algebraic groups; non-commutative algebraic geometry; representation theory of finite groups and cohomology; the structure of special classes of rings.
Author : F. van Oystaeyen,A. Verschoren
Publisher : Springer
Page : 312 pages
File Size : 50,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540390572