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 comprises 5 evaluate articles, 3 within the Al­ gebra half and within the Geometry half, surveying the fields of ring conception, modules, and lattice thought within the former, and people of crucial geometry and differential-geometric equipment within the calculus of adaptations within the latter. The literature lined is essentially that released in 1965-1968. v CONTENTS ALGEBRA RING concept L. A. Bokut', okay. A. Zhevlakov, and E. N. Kuz'min § 1. Associative jewelry. . . . . . . . . . . . . . . . . . . . three § 2. Lie Algebras and Their Generalizations. . . . . . . thirteen ~ three. replacement and Jordan jewelry. . . . . . . . . . . . . . . . 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 jewelry. . . . . . . . . . . . sixty six § four. Quasi-Frobenius earrings and Their Generalizations. . seventy one § five. a few points of Homological Algebra . . . . . . . . . . seventy five § 6. Endomorphism earrings . . . . . . . . . . . . . . . . . . . . . eighty three § 7. different elements. . . . . . . . . . . . . . . . . . . 87 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , ninety one LATTICE concept M. M. Glukhov, 1. V. Stelletskii, and T. S. Fofanova § 1. Boolean Algebras . . . . . . . . . . . . . . . . . . . . . " 111 § 2. identification and Defining kinfolk in Lattices . . . . . . one hundred twenty § three. Distributive Lattices. . . . . . . . . . . . . . . . . . . . . 122 vii viii CONTENTS § four. Geometrical elements and the comparable Investigations. . . . . . . . . . . . • . . • . . . . . . . . . • a hundred twenty five § five. Homological elements. . . . . . . . . . . . . . . . . . . . . . 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 features. . . . . . . . . . . . . . . . . . . . . . 137 § 10. Partially-Ordered units. . . . . . . . . . . . . . . . . . . . 141 § eleven. different Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY essential GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .

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42(3): 489-496 (1967). 348. P. Holgate, Genetic algebras associated with polyploidy. Proc. Edinburgh Math. , 15(0:1-9 (1966). 349. P. Holgate, The genetic algebra k linked loci. Proc. London Math. , 18(3): 315-327 (1968). 350. P. Holgate, Jordan algebras arising in population genetics. Proc. Edinburgh Math. , 15(4):291-294 (1967). 351. W. G. van Hoorn and B. van Rootselaar, Fundamental notions in the theory of seminearrings. , 18(1-2):65-78 (1966). 41 RING THEORY 352. Pang-chieh Hsieh, Rings with semi-minimum condition.

Edinburgh Math. , 15(0:1-9 (1966). 349. P. Holgate, The genetic algebra k linked loci. Proc. London Math. , 18(3): 315-327 (1968). 350. P. Holgate, Jordan algebras arising in population genetics. Proc. Edinburgh Math. , 15(4):291-294 (1967). 351. W. G. van Hoorn and B. van Rootselaar, Fundamental notions in the theory of seminearrings. , 18(1-2):65-78 (1966). 41 RING THEORY 352. Pang-chieh Hsieh, Rings with semi-minimum condition. Scientia sinica, 14(3): 343-362 (1965). 353. M. M. Humm, On a class of right alternative rings without nilpontent ideals.

Canad. J. , 20(2):465-473 (1968). 180. M. Becheanu, Remarque sur les radicals speciaux. Rev. roumaine math. , 10 (3):357 -360 (1965). 181. J. C. Beidleman, Nonsemi-simple distributively generated near-rings with minimum condition. Math. , 170(3):206-213 (1967). 182. J. C. Beidleman, On the theory of radicals of distributively generated near-rings. 1. The primitive radical. Math. , 173(2):89-101 (1967). 183. J. C. Beidleman, On the theory of radicals of distributively generated near-rings. II. The nil-radical.

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