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.