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.)

This quantity comprises 5 evaluation 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 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', ok. A. Zhevlakov, and E. N. Kuz'min § 1. Associative earrings. . . . . . . . . . . . . . . . . . . . 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 on. . . . . . . . . . . . . . . . . . . sixty two § three. Homological type of earrings. . . . . . . . . . . . sixty six § four. Quasi-Frobenius earrings and Their Generalizations. . seventy one § five. a few elements of Homological Algebra . . . . . . . . . . seventy five § 6. Endomorphism jewelry . . . . . . . . . . . . . . . . . . . . . eighty three § 7. different elements. . . . . . . . . . . . . . . . . . . 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 . . . . . . one hundred twenty § three. Distributive Lattices. . . . . . . . . . . . . . . . . . . . . 122 vii viii CONTENTS § four. Geometrical points and the comparable Investigations. . . . . . . . . . . . • . . • . . . . . . . . . • a 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 facets. . . . . . . . . . . . . . . . . . . . . . 137 § 10. Partially-Ordered units. . . . . . . . . . . . . . . . . . . . 141 § eleven. different Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY vital GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .

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6. V. r. Andriyanov, "Periodic Hamiltonian rings," Mat. , 74(2):241-261 (1967). V. I. Andriyanov, "Composite r -rings," Sverdl. Gos. Ped. , Vol. 54, 12- 21 (1967). V. I. Andriyanov, "Composite Hamiltonian rings," Mat. Zap. , 5(3):15-30 (1966). V. r. Andriyanov and P. A. Freidman, "Hamiltonian rings," Uch. Zap. Sverdl. Gos. Ped. , Vol. 31, 3-23 (1965). V. A. Andrunakievich and V. 1. Arnautov, "lnvertibility in topological rings," Dokl. Akad. Nauk SSSR, 170(4):755-758 (1966). v. A. Andrunakievich, V.

Straus, Infinite sums in algebraic structures. pacif. J. , 15(1):181-190 (1965). 398. Y. Kawada, On Kothe's problem concerning algebras for which every indecomposable module is cyclic. Ill. Sci. Repts. Tokyo Kyoiku Daigaku A, 8(196-201): 1-250 (1965). 399. S. M. Kaye, Ring theoretic properties of matrix rings. Canad. Math. , 10(3):365-374 (1967). RING THEORY 43 400. O. H. Kegel, On rings that are sums of two subrings. J. Algebra, 1(2):103-109 (1964). 401. A. Kertesz, On the existence of a left unit element in a noetherian or in an artinian ring.

Akad. Nauk SSSR, Ser. , 31(5):1057-1090 (1967). V. A. Andrunakievich and Yu. M. Ryabukhin, "Rings without nilpotent elements and completely prime ideals," Dok!. Akad. Nauk SSSR, 180(1):9-11 (1968). V. I. Amautov, "Topologically weakly regular rings," in: Investigations in Algebra and Mathematical Analysis [in Russian], Kartya Moldovenyaske, Kishinev (1965). pp. 3-10. V. I. Amautov, "Topological rings with a gi ven local weight," in: Investigations in General Algebra [in Russian], Kishinev (1965), pp.

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