Download Algebra and Geometry by L. A. Bokut’, K. A. Zhevlakov, E. N. Kuz’min (auth.), R. V. PDF

By L. A. Bokut’, K. A. Zhevlakov, E. N. Kuz’min (auth.), R. V. Gamkrelidze (eds.)

This quantity includes 5 overview articles, 3 within the Al­ gebra half and within the Geometry half, surveying the fields of ring idea, modules, and lattice concept within the former, and people of fundamental geometry and differential-geometric tools within the calculus of adaptations within the latter. The literature lined is essentially that released in 1965-1968. v CONTENTS ALGEBRA RING thought L. A. Bokut', okay. A. Zhevlakov, and E. N. Kuz'min § 1. Associative earrings. . . . . . . . . . . . . . . . . . . . three § 2. Lie Algebras and Their Generalizations. . . . . . . thirteen ~ three. replacement and Jordan earrings. . . . . . . . . . . . . . . . 18 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 MODULES A. V. Mikhalev and L. A. Skornyakov § 1. Radicals. . . . . . . . . . . . . . . . . . . fifty nine § 2. Projection, Injection, and so on. . . . . . . . . . . . . . . . . . . sixty two § three. Homological type of jewelry. . . . . . . . . . . . sixty six § four. Quasi-Frobenius earrings and Their Generalizations. . seventy one § five. a few points of Homological Algebra . . . . . . . . . . seventy five § 6. Endomorphism jewelry . . . . . . . . . . . . . . . . . . . . . eighty three § 7. different facets. . . . . . . . . . . . . . . . . . . 87 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , ninety one LATTICE thought M. M. Glukhov, 1. V. Stelletskii, and T. S. Fofanova § 1. Boolean Algebras . . . . . . . . . . . . . . . . . . . . . " 111 § 2. id and Defining family members in Lattices . . . . . . a hundred and twenty § three. Distributive Lattices. . . . . . . . . . . . . . . . . . . . . 122 vii viii CONTENTS § four. Geometrical facets and the comparable Investigations. . . . . . . . . . . . • . . • . . . . . . . . . • a hundred twenty five § five. Homological facets. . . . . . . . . . . . . . . . . . . . . . 129 § 6. Lattices of Congruences and of beliefs of a Lattice . . 133 § 7. Lattices of Subsets, of Subalgebras, and so on. . . . . . . . . 134 § eight. Closure Operators . . . . . . . . . . . . . . . . . . . . . . . 136 § nine. Topological features. . . . . . . . . . . . . . . . . . . . . . 137 § 10. Partially-Ordered units. . . . . . . . . . . . . . . . . . . . 141 § eleven. different Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY quintessential GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .

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100(2):97-105 (1967). 189. J. C. Beidleman and R. H. Cox, Topological near-rings. Arch. , 18(5): 485-492 (1967). 190. L. P. Belluce and S. K. Jain, Prime rings with a one-sided ideal satisfying a polynomial identity. Pacif. ]. , 24(3):421-424 (1968). 191. L. P. Belluce, I. N. Herstein, and S. K. Jain, Generalized commutative rings. Nagoya Math. , 27(1);1-5 (1966). 192. A. Bergmann, Hauptnorm und Struktur von Algebren. J. reine und angew. , 222(3/4):160 -194 (1966). 193. P. Bernat, "Sur Ie corps enveloppant d'une algebre de Lie resoluble," Bull.

Colomb. , 1(3):2932 (1967). 156. T. A. Anderson, A note on derivations of commutative algebras. Proc. Amer. Math. , 17(5): 1199-1202 (1966). 157. T. Anderson, N. Divinsky, and A. Sulinski, Hereditary radicals in associative and alternative rings. Ganad. I. , 17(4):594-603 (1965). 158. S. Andreadakis, On the derivations and automorphisms of Lie algebras. Arch. , 17 (1):36-43 (1966). 159. E. P. Armendariz, On radical extensions of rings. J. Austral. Math. , 7(4): 552-554 (1967). 160. E. P. Armendariz and W.

RING THEORY 31 116. L. A. Skornyakov, "Locally bicompact biregular rings (supplement)," Mat. , 69(4):663 (1966). 117. L. A. Skornyakov, "The Elizarov quotient ring and the localization principle," Mat. Zametki, 1(3):263-268 (1967). 118. L. A. Skornyakov, "Left-chain rings," Izv. Vyssh. Uchebn. 4, 114-117 (1966). 119. D. A. Suprunenko and V. I. Monastyrnyi, "Silov subgroups of the multiplicative group of a division ring," DokI. Akad. Nauk BSSR, 9(4):217-218 (1965). 120. D. A. Suprunenko and R. I.

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