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 evaluate articles, 3 within the Al­ gebra half and within the Geometry half, surveying the fields of ring thought, modules, and lattice concept within the former, and people of vital geometry and differential-geometric tools within the calculus of adaptations within the latter. The literature coated is essentially that released in 1965-1968. v CONTENTS ALGEBRA RING idea 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 forth. . . . . . . . . . . . . . . . . . . sixty two § three. Homological type of earrings. . . . . . . . . . . . sixty six § four. Quasi-Frobenius earrings and Their Generalizations. . seventy one § five. a few features of Homological Algebra . . . . . . . . . . seventy five § 6. Endomorphism earrings . . . . . . . . . . . . . . . . . . . . . eighty three § 7. different points. . . . . . . . . . . . . . . . . . . 87 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , ninety one LATTICE conception M. M. Glukhov, 1. V. Stelletskii, and T. S. Fofanova § 1. Boolean Algebras . . . . . . . . . . . . . . . . . . . . . " 111 § 2. id and Defining kin in Lattices . . . . . . one hundred twenty § three. Distributive Lattices. . . . . . . . . . . . . . . . . . . . . 122 vii viii CONTENTS § four. Geometrical facets and the comparable Investigations. . . . . . . . . . . . • . . • . . . . . . . . . • one hundred twenty five § five. Homological points. . . . . . . . . . . . . . . . . . . . . . 129 § 6. Lattices of Congruences and of beliefs of a Lattice . . 133 § 7. Lattices of Subsets, of Subalgebras, and so forth. . . . . . . . . 134 § eight. Closure Operators . . . . . . . . . . . . . . . . . . . . . . . 136 § nine. Topological elements. . . . . . . . . . . . . . . . . . . . . . 137 § 10. Partially-Ordered units. . . . . . . . . . . . . . . . . . . . 141 § eleven. different Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY necessary GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .

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427. K. Koh and A. Mewborn, The weak radical of a ring. Proc. Amer. Math. , 18(3):554-559 (1967). 428. K. Koh and A. Mewborn, Prime rings with maximal annihilator and maximal complement right ideals. Proc. Amer. Math. , 16(5):1073-1076 (1965). 429. c. W. Kohls, Properties inherited by ring extensions. Mich. Math. , 12(4): 399-404 (1965). 430. c. W. Kohls, On convex ideals. Proc. Amer. Math. , 18(2):359-363 (1967). 431. B. Kolman, Semi-modular Lie algebras. 1. Sci. , Ser. A, Div. , 29(2):149-163 (1961).

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Hirata and K. Sugano, On semisimple extensions and separable extensions over'non-commutative rings. J. Math. Soc. Japan, 18(4):360-373 (1968). 345. R. D. Hirsch, A note on non-commutative polynomial rings subject to degreepreservation. J. London Math. , 42(2J:3311-335 (196'7). 346. G. Hochschild. An addition to Ado's theorem. Proc. Amer. Math. , 17(2): 531-533 (1966). 347. P. Holgate, Sequences of powers in genetic algebras. J. London Math. , 42(3): 489-496 (1967). 348. P. Holgate, Genetic algebras associated with polyploidy.

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