Algebra and Geometry (Paperback, Softcover reprint of the original 1st ed. 1972)

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 . . . . . . . . .

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Progress in Mathematics, 12
Release date:	December 2012
First published:	1972
Authors:	R. V Gamkrelidze
Dimensions:	229 x 152 x 14mm (L x W x T)
Format:	Paperback
Pages:	254
Edition:	Softcover reprint of the original 1st ed. 1972
ISBN-13:	978-1-4757-0509-6
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General
LSN:	1-4757-0509-3
Barcode:	9781475705096

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