株式会社極東書店トップ ＞ 商品一覧 ＞ Algebra and Geometry. Softcover reprint of the original 1st ed. 1972.
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Algebra and Geometry. Softcover reprint of the original 1st ed. 1972.
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| 著者・編者 | Gamkrelidze, R. V., |
|---|---|
| シリーズ | Progress in Mathematics |
| 出版社 | (Springer-Verlag New York Inc., US) |
| 出版年月 | 2012 |
| ページ数 | 254 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-18812＞ |
解説
This volume contains five review articles, three in the Al- gebra part and two in the Geometry part, surveying the fields of ring theory, modules, and lattice theory in the former, and those of integral geometry and differential-geometric methods in the calculus of variations in the latter. The literature covered is primarily that published in 1965-1968. v CONTENTS ALGEBRA RING THEORY L. A. Bokut', K. A. Zhevlakov, and E. N. Kuz'min ? 1. Associative Rings. . . . . . . . . . . . . . . . . . . . 3 ? 2. Lie Algebras and Their Generalizations. . . . . . . 13 ~ 3. Alternative and Jordan Rings. . . . . . . . . . . . . . . . 18 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 MODULES A. V. Mikhalev and L. A. Skornyakov ? 1. Radicals. . . . . . . . . . . . . . . . . . . 59 ? 2. Projection, Injection, etc. . . . . . . . . . . . . . . . . . . 62 ? 3. Homological Classification of Rings. . . . . . . . . . . . 66 ? 4. Quasi-Frobenius Rings and Their Generalizations. . 71 ? 5. Some Aspects of Homological Algebra . . . . . . . . . . 75 ? 6. Endomorphism Rings . . . . . . . . . . . . . . . . . . . . . 83 ? 7. Other Aspects. . . . . . . . . . . . . . . . . . . 87 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , 91 LATTICE THEORY M. M. Glukhov, 1. V. Stelletskii, and T. S. Fofanova ? 1. Boolean Algebras . . . . . . . . . . . . . . . . . . . . . " 111 ? 2. Identity and Defining Relations in Lattices . . . . . . 120 ? 3. Distributive Lattices. . . . . . . . . . . . . . . . . . . . . 122 vii viii CONTENTS ? 4. Geometrical Aspects and the Related Investigations. . . . . . . . . . . . * . . * . . . . . . . . . * 125 ? 5. Homological Aspects. . . . . . . . . . . . . . . . . . . . . . 129 ? 6. Lattices ofCongruences and of Ideals of a Lattice . . 133 ? 7. Lattices of Subsets, of Subalgebras, etc. . . . . . . . . 134 ? 8. Closure Operators . . . . . . . . . . . . . . . . . . . . . . . 136 ? 9. Topological Aspects. . . . . . . . . . . . . . . . . . . . . . 137 ? 10. Partially-Ordered Sets. . . . . . . . . . . . . . . . . . . . 141 ? 11. Other Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY INTEGRAL GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .