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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 of Congruences 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 . . . . . . . . .
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Algebra.- Ring Theory.- Modules.- Lattice Theory.- Geometry.- Integral Geometry.- Differential-Geometric Methods in the Calculus of Variations.
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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 . . . . . . . . .Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 268 pp. Englisch. Codice articolo 9781475705096
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