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Algebra and Geometry

  • R. V. Gamkrelidze

Part of the Progress in Mathematics book series (PM, volume 12)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Algebra

    1. Front Matter
      Pages 1-1
    2. L. A. Bokut’, K. A. Zhevlakov, E. N. Kuz’min
      Pages 3-58
    3. A. V. Mikhalev, L. A. Skornyakov
      Pages 59-109
    4. M. M. Glukhov, I. V. Stelletskii, T. S. Fofanova
      Pages 111-170
  3. Geometry

    1. Front Matter
      Pages 171-171
    2. G. I. Drinfel’d
      Pages 173-215

About this book

Introduction

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 . . . . . . . . .

Keywords

Boolean algebra Calc Lattice Lie Morphism algebra associative ring calculus congruence endomorphism ring form identity lie algebra review ring

Editors and affiliations

  • R. V. Gamkrelidze
    • 1
  1. 1.V. A. Steklov Mathematics InstituteAcademy of Sciences of the USSRMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-0507-2
  • Copyright Information Springer-Verlag US 1972
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-0509-6
  • Online ISBN 978-1-4757-0507-2
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site
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