Download e-book for kindle: Algebra and Geometry by L. A. Bokut’, K. A. Zhevlakov, E. N. Kuz’min (auth.), R. V.

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

ISBN-10: 1475705077

ISBN-13: 9781475705072

ISBN-10: 1475705093

ISBN-13: 9781475705096

This quantity includes 5 overview articles, 3 within the Al­ gebra half and within the Geometry half, surveying the fields of ring conception, modules, and lattice conception within the former, and people of critical geometry and differential-geometric equipment within the calculus of diversifications within the latter. The literature coated is essentially that released in 1965-1968. v CONTENTS ALGEBRA RING concept L. A. Bokut', ok. A. Zhevlakov, and E. N. Kuz'min § 1. Associative earrings. . . . . . . . . . . . . . . . . . . . three § 2. Lie Algebras and Their Generalizations. . . . . . . thirteen ~ three. substitute and Jordan jewelry. . . . . . . . . . . . . . . . 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 earrings. . . . . . . . . . . . sixty six § four. Quasi-Frobenius jewelry and Their Generalizations. . seventy one § five. a few facets of Homological Algebra . . . . . . . . . . seventy five § 6. Endomorphism jewelry . . . . . . . . . . . . . . . . . . . . . eighty three § 7. different features. . . . . . . . . . . . . . . . . . . 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 elements and the similar Investigations. . . . . . . . . . . . • . . • . . . . . . . . . • one hundred twenty five § five. Homological features. . . . . . . . . . . . . . . . . . . . . . 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 points. . . . . . . . . . . . . . . . . . . . . . 137 § 10. Partially-Ordered units. . . . . . . . . . . . . . . . . . . . 141 § eleven. different Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY quintessential GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .

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Proc. Amer. Math. , 18(5):898-901 (1967). 411. M. A. Knus, Sur une classe d 'algebres filtrees. Comment. math. , 42(2): 111-131 (1967). 412. D. E. Knuth, Finite semifields and projective planes. J. Algebra, 2(2):182-217 (1965). 413. S. Kobayashi and T. Nagano, On filtered Lie algebras and geometric structures. Ill. J. Math. , 14(4):697-707 (1965). 414. S. Kobayashi and T. Nagano, A Report on Filtered Lie Algebras, Proceedings U. -Japan Sem. , Ltd. (1966), pp. 63-70. 415. M. Koecher, On homogeneous algebras.

Akad. , 28(2):202-212 (1966). Ain, A:n, 372. N. R. Jacobson, Homomorphism of Jordan rings of self-adjoint elements. Trans. Amer. Math. , 72:310-322 (1952). 373. s. K. Jain, Polynomial rings with a pivotal monomial. Proc. Amer. Math. , 17(4):942-945 (1966). 374. S. K. Jain, Rings with constraints. Math. , 34(3-4):175-178 (1966). 42 L. A. BOKUT', K. A. ZHEVLAKOV, AND E. N. KUZ'MIN 375. S. K. Jain, On unitary of II-unitary rings. Publs. , 11(1):241-244 (1964). 376. J. P. Jans, On orders in quasi-Frobenius rings.

Student, 32(1-2):7-10 (1964). 358. M. Ikeda, Ober die einstufig nichtkommutativen Ringe. Nagoya Math. , 27(1): 371-379 (1966). 359. E. C. Ingraham, On the existence of inertial subalgebras. Doct. diss. Univ. Ore .. ; Dissert. , 26(8):4690-4691 (1966). 360. E. C. Ingraham, Inertial subalgebras of algebras over commutative rings. Trans. Amer. Math. , 124(1):77-93 (1966). 361. D. B. Ion, Asupra algebrelor Jordan de tip A. Studii si cercetari mat. Acad. RPR, 17(2):301-310 (1965). 362. D. B. Ion, Asupra unor proprietli~i ale constantelor de structura ale algebrelor Jordan de tip A.

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


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