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  • 1
    Online Resource
    Online Resource
    Amsterdam ; : Elsevier,
    UID:
    almahu_9947367818202882
    Format: 1 online resource (543 p.)
    ISBN: 1-280-64187-8 , 9786610641871 , 0-08-046249-9
    Series Statement: Handbook of algebra ; 4
    Content: 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
    Note: Description based upon print version of record. , Cover; Contents; Preface; Basic philosophy; Planning; The individual chapters; The present; The future; Outline of the Series; Philosophy and principles of the Handbook of Algebra; Section 1. Linear algebra. Fields. Algebraic number theory; Section 2. Category theory. Homological and homotopical algebra. Methods from logic; Section 3. Commutative and associative rings and algebras; Section 4. Other algebraic structures. Nonassociative rings and algebras. Commutative and associative algebras with extra structure; Section 5. Groups and semigroups; Section 6. Representation and invariant theory , Section 7. Machine computation. Algorithms. TablesSection 8. Applied algebra; Section 9. History of algebra; List of Contributors; Section 2C. Algebraic K-theory; Higher Algebraic K-Theory; Introduction; Simplicial objects, classifying spaces, and spectra; Definitions of and relations between several higher algebraic K-theories (for rings); Higher K-theory of exact, symmetric monoidal and Waldhausen categories; Some fundamental results and exact sequences in higher K-theory; Higher K-theory and connections to Galois, étale and motivic cohomology theories , Higher K-theory of rings of integers in local and global fieldsHigher K-theory of orders, group-rings and modules over `EI'-categories; Equivariant higher algebraic K-theory together with relative generalizations; Acknowledgement; References; Section 3B. Associative Rings and Algebras; Filter Dimension; Introduction; Filter dimension of algebras and modules; The first filter inequality; Krull, Gelfand-Kirillov and filter dimensions of simple finitely generated algebras , Filter dimension of the ring of differential operators on a smooth irreducible affine algebraic variety (proof of Theorem 4.3)Multiplicity for the filter dimension, holonomic modules over simple finitely generated algebras; Filter dimension and commutative subalgebras of simple finitely generated algebras and their division algebras; Filter dimension and isotropic subalgebras of Poisson algebras; References; Section 4E. Lie Algebras; Gelfand-Tsetlin Bases for Classical Lie Algebras; Introduction; Gelfand-Tsetlin bases for representations of gln; Weight bases for representations of oN and sp2n , Gelfand-Tsetlin bases for representations of oNAcknowledgements; References; Section 4H. Rings and Algebras with Additional Structure; Hopf Algebras; Introduction; Part 1. Basic concepts; Coalgebras and comodules; Hopf algebras; Modules and comodules for Hopf algebras; Normal Hopf subalgebras, quotients and extensions; Special Hopf algebras; Twisting in Hopf algebras; Constructing new Hopf algebras from known ones; Part 2. Fundamental theorems; The fundamental theorem for Hopf modules; Integrals; Maschke's theorem; The antipode; The Nichols-Zoeller theorem; Kac-Zhu theorem , Part 3. Actions and coactions , English
    Additional Edition: ISBN 0-444-52213-1
    Language: English
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Book
    Book
    Amsterdam [u.a.] : Elsevier
    Show associated volumes
    UID:
    gbv_520846478
    Format: XXIII, 518 S. , graph. Darst.
    Edition: 1. ed.
    ISBN: 0444522131 , 9780444522139
    Note: Includes bibliographical references and index
    In: Vol. 4
    Additional Edition: Erscheint auch als Online-Ausgabe Handbook of algebra ; 4 Amsterdam : Elsevier North-Holland, 2006 ISBN 0444522131
    Additional Edition: ISBN 9780444522139
    Additional Edition: ISBN 1280641878
    Additional Edition: ISBN 9781280641879
    Language: English
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  • 3
    Online Resource
    Online Resource
    Amsterdam : Elsevier North-Holland
    Show associated volumes
    UID:
    gbv_630035679
    Format: Online Ressource
    Edition: 1. ed.
    Edition: Amsterdam Elsevier Science & Technology Elsevier e-book collection on ScienceDirect Electronic reproduction; Mode of access: World Wide Web
    Edition: ScienceDirect
    ISBN: 0444522131 , 9780444522139 , 1280641878 , 9781280641879
    Content: 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
    Content: 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
    Note: Includes bibliographical references and indexes , Vol. 2: 1st ed , v. 1. Linear algebra, fields, algebraic number theory. , Preface -- Outline of the Series -- List of Contributors -- Section 2C. Algebraic K-theory -- Higher Algebraic K-theory (A. Kuku) -- Section 3B. Associative Rings and Algebras -- Filter Dimension (V.V. Bavula) -- Section 4E. Lie Algebras -- Gelfand-Tsetlin Bases for Classical Lie Algebras (A.I. Molev) -- Section 4H. Rings and Algebras with Additional Structure -- Hopf Algebras (M. Cohen, S. Gelaki and S. Westreich) -- Difference Algebra (A.B. Levin) -- Section 5A. Groups and Semigroups -- Reflection Groups (M. Geck and G. Malle) -- Hurwitz Groups and Hurwitz Generation (M.C. Tamburini and M. Vsemirnov) -- Survey on Braids (V. Vershinin) -- Groups with Finiteness Conditions (V.I. Senashov) -- Index. , Electronic reproduction; Mode of access: World Wide Web
    In: 4
    Additional Edition: ISBN 0444822127
    Additional Edition: ISBN 9780444822123
    Additional Edition: Erscheint auch als Druck-Ausgabe Handbook of algebra ; Vol. 4 Amsterdam [u.a.] : Elsevier, 2006 ISBN 0444522131
    Additional Edition: ISBN 9780444522139
    Additional Edition: Erscheint auch als Druck-Ausgabe Handbook of algebra ; 4 Amsterdam : Elsevier North-Holland, 2006 ISBN 0444522131
    Additional Edition: ISBN 9780444522139
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Electronic books ; Electronic books
    URL: Volltext  (lizenzpflichtig)
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