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TitleAlgebra and Geometry [electronic resource] / edited by R. V. Gamkrelidze
ImprintBoston, MA : Springer US : Imprint: Springer, 1972
Connect tohttp://dx.doi.org/10.1007/978-1-4757-0507-2
Descript IX, 254 p. online resource

SUMMARY

This volume contains five review articles, three in the Alยญ 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 ยง 1. Associative Rings. . . . . . . . . . . . . . . . . . . . 3 ยง 2. Lie Algebras and Their Generalizations. . . . . . . 13 ̃ 3. Alternative and Jordan Rings. . . . . . . . . . . . . . . . 18 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 MODULES A. V. Mikhalev and L. A. Skornyakov ยง 1. Radicals. . . . . . . . . . . . . . . . . . . 59 ยง 2. Projection, Injection, etc. . . . . . . . . . . . . . . . . . . 62 ยง 3. Homological Classification of Rings. . . . . . . . . . . . 66 ยง 4. Quasi-Frobenius Rings and Their Generalizations. . 71 ยง 5. Some Aspects of Homological Algebra . . . . . . . . . . 75 ยง 6. Endomorphism Rings . . . . . . . . . . . . . . . . . . . . . 83 ยง 7. Other Aspects. . . . . . . . . . . . . . . . . . . 87 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , 91 LATTICE THEORY M. M. Glukhov, 1. V. Stelletskii, and T. S. Fofanova ยง 1. Boolean Algebras . . . . . . . . . . . . . . . . . . . . . " 111 ยง 2. Identity and Defining Relations in Lattices . . . . . . 120 ยง 3. Distributive Lattices. . . . . . . . . . . . . . . . . . . . . 122 vii viii CONTENTS ยง 4. Geometrical Aspects and the Related Investigations. . . . . . . . . . . . โ{128}ข . . โ{128}ข . . . . . . . . . โ{128}ข 125 ยง 5. Homological Aspects. . . . . . . . . . . . . . . . . . . . . . 129 ยง 6. Lattices of Congruences and of Ideals of a Lattice . . 133 ยง 7. Lattices of Subsets, of Subalgebras, etc. . . . . . . . . 134 ยง 8. Closure Operators . . . . . . . . . . . . . . . . . . . . . . . 136 ยง 9. Topological Aspects. . . . . . . . . . . . . . . . . . . . . . 137 ยง 10. Partially-Ordered Sets. . . . . . . . . . . . . . . . . . . . 141 ยง 11. Other Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY INTEGRAL GEOMETRY G. 1. Drinfel'd Preface . . . . . . . .


CONTENT

Algebra -- Ring Theory -- Modules -- Lattice Theory -- Geometry -- Integral Geometry -- Differential-Geometric Methods in the Calculus of Variations


Mathematics Algebra Mathematics Algebra



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