Handbook of algebra  v. 1 ~ v. 6

edited by M. Hazewinkel

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 of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes

「Nielsen BookData」より

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. It features thorough and practical source for information. It also provides in-depth coverage of new topics in algebra. It includes references to relevant articles, books and lecture notes.

「Nielsen BookData」より

Algebra, as we know it today, consists of many different ideas, concepts and results. Estimates 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. 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 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 first volume articles from three 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.

「Nielsen BookData」より

Algebra, as we know it today, consists of many different ideas, concepts and results. The 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.In this title, 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. The 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. This title presents thorough and practical source of information. It provides in-depth coverage of new topics in algebra. It includes references to relevant articles, books and lecture notes.

「Nielsen BookData」より

Algebra, as we know it today, consists of many different ideas, concepts and results. A rough estimate of the number of these different "items" would be somewhere between 50,000 and 200,000. Many of them have been named and many more could (and perhaps should) have a "name" or a convenient designation. In addition to primary information, this handbook provides references to relevant articles, books and lecture notes. It will publish articles as they are received and thus the reader will find in this second volume articles from five 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. One of the main aims of the Handbook is to provide professional mathematicians with sufficient information for working in areas other than their own specialist fields.

「Nielsen BookData」より

[目次]

  • 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

「Nielsen BookData」より

[目次]

  • Preface. Section 1A. Linear Algebra. Van der Waerden conjecture and applications (G.P. Egorychev). Random matrices (V.L. Girko). Matrix equations. Factorization of matrix polynomials (A.N. Malyshev). Matrix functions (L. Rodman). Section 1B. Linear (In)dependence. Matroids (J.P.S. Kung). Section 1D. Fields, Galois Theory, and Algebraic Number Theory. Higher derivation Galois theory of inseparable field extensions (J.K. Deveney, J.N. Mordeson). Theory of local fields. Local class field theory. Higher local class field theory (I.B. Fesenko). Infinite Galois theory (M. Jarden). Finite fields and their applications (R. Lidl, H. Niederreiter). Global class field theory (W. Narkiewicz). Finite fields and error correcting codes (H. van Tilborg). Section 1F. Generalizations of Fields and Related Objects. Semi-rings and semi-fields (U. Hebisch, H.J. Weinert). Near-rings and near-fields (G.F. Pilz). Section 2A. Category Theory. Topos theory (S. MacLane, I. Moerdijk). Categorical structures (R.H. Street). Section 2B. Homological Algebra. Cohomology. Cohomological Methods in Algebra. Homotopical Algebra. The cohomology of groups (J.F. Carlson). Relative homological algebra. Cohomology of categories, posets, and coalgebras (A.I. Generalov). Homotopy and homotopical algebra (J.F. Jardine). Derived categories and their uses (B. Keller). Section 3A. Commutative Rings and Algebras. Ideals and modules (J.-P. Lafon). Section 3B. Associative Rings and Algebras. Polynomial and power series rings. Free algebras, firs and semifirs (P.M. Cohn). Simple, prime, and semi-prime rings (V.K. Kharchenko). Algebraic microlocalization and modules with regular singularities over filtered rings (A.R.P. van den Essen). Frobenius rings (K. Yamagata). Subject Index.

「Nielsen BookData」より

[目次]

  • Preface. Outline of the Series. List of Contributors. Section 2A. Category Theory. Some aspects of categories in computer science (P.J. Scott). Algebra, categories, and databases (B. Plotkin). Section 2B. Homological Algebra. Cohomology. Cohomological Methods in Algebra. Homotopical Algebra. Homology for the algebras of analysis (A.Ya. Helemskii). Section 2D. Model Theoretic Algebra. Stable groups (F.O. Wagner). Section 3A. Commutative Rings and Algebras. Artin approximation (D. Popescu). Section 3B. Associative Rings and Algebras. Fixed rings and noncommutative invariant theory (V.K. Kharchenko). Modules with distributive submodule lattice (A.A. Tuganbaev). Serial and semidistributive modules and rings (A.A. Tuganbaev). Modules with the exchange property and exchange rings (A.A. Tuganbaev). Separable algebras (F. Van Oystaeyen). Section 3D. Deformation Theory of Rings and Algebras. Varieties of Lie algebra laws (Yu. Khakimdjanov). Section 4D. Varieties of Algebras, Groups, ... Varieties of algebras (V.A. Artamonov). Section 4E. Lie Algebras. Infinite-dimensional Lie superalgebras (Yu. Bahturin, A. Mikhalev, M. Zaicev). Nilpotent and solvable Lie algebras (M. Goze, Yu. Khakimdjanov). Section 5A. Groups and Semigroups. Infinite Abelian groups: Methods and results (A.V. Mikhalev, A.P. Mishina). Section 6C. Representation Theory of 'Continuous Groups' (Linear Algebraic Groups, Lie groups, Loop Groups, ...) and the Corresponding Algebras. Infinite-dimensional representations of the quantum algebras (A.U. Klimyk). Section 6D. Abstract and Functorial Representation Theory. Burnside rings (S. Bouc). A guide to Mackey Functors (P. Webb). Subject Index.

「Nielsen BookData」より

この本の情報

書名 Handbook of algebra
著作者等 Hazewinkel, Michiel
巻冊次 v. 1
v. 2
v. 3
v. 4
v. 5
v. 6
出版元 Elsevier Science
刊行年月 c1996-
ページ数 v.
大きさ 24-25 cm
ISBN 044450396X
0444512640
0444822127
9780444531018
9780444532572
9780444522139
ISSN 15707954
NCID BA26932197
※クリックでCiNii Booksを表示
言語 英語
出版国 オランダ
この本を: 
このエントリーをはてなブックマークに追加

このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想