Progress in Mathematics

Algebra and Geometry
1971
ISBN: 978-1-4684-3308-1
Verlag: Springer US

Buch, Englisch, Band 9, 253 Seiten, Paperback, Format (B × H): 152 mm x 229 mm, Gewicht: 393 g

Reihe: Progress in Mathematics

This volume contains five review articles, two in the Algebra part and three in the Geometry part, surveying the fields of cate­ gories and class field theory, in the Algebra part, and of Finsler spaces, structures on differentiable manifolds, and packing, cover­ ing, etc., in the Geometry part. The literature covered is primar­ Hy that published in 1964-1967. Contents ALGEBRA CATEGORIES. 3 M. S. Tsalenko and E. G. Shul'geifer § 1. Introduction. 3 § 2. Foundations of the Theory of Categories. 4 § 3. Fundamentals of the Theory of Categories. 6 § 4. Embeddings of Categories. 14 § 5. Representations of Categories. 16 § 6. Axiomatic Characteristics of Algebraic Categories. 18 § 7. Reflective Subcategories; Varieties. 20 § 8. Radicals in Categories. 24 § 9. Categories with Involution. 29 § 10. Universal Algebras in Categories. 30 § 11. Categories with Multiplication. 34 § 12. Duality of Functors. 37 § 13. Homotopy Theory. 39 § 14. Homological Algebra in Categories. 41 § 15. Concrete Categories. 44 § 16. Generalizations. 45 Literature Cited. 47 CLASS FIELD THEORY. FIELD EXTENSIONS. 59 S. P. Demushkin 66 Literature Cited vii CONTENTS viii GEOMETRY 75 FINSLER SPACES AND THEIR GENERALIZATIONS.

Zielgruppe

Research

Autoren/Hrsg.

Gamkrelidze, R. V.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

Algebra.- Categories.- Class field theory. Field extensions.- Geometry.- Finsler Spaces and their Generalizations.- Structures on Differentiable Manifolds.- Packings, Coverings, Partitionings, and Certain other Distributions in Spaces of Constant Curvature.