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 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 thought L. A. Bokut', ok. 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 earrings. . . . . . . . . . . . sixty six § four. Quasi-Frobenius earrings and Their Generalizations. . seventy one § five. a few points of Homological Algebra . . . . . . . . . . seventy five § 6. Endomorphism jewelry . . . . . . . . . . . . . . . . . . . . . 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 family in Lattices . . . . . . a hundred and twenty § three. Distributive Lattices. . . . . . . . . . . . . . . . . . . . . 122 vii viii CONTENTS § four. Geometrical points and the similar Investigations. . . . . . . . . . . . • . . • . . . . . . . . . • a hundred twenty five § five. Homological facets. . . . . . . . . . . . . . . . . . . . . . 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 points. . . . . . . . . . . . . . . . . . . . . . 137 § 10. Partially-Ordered units. . . . . . . . . . . . . . . . . . . . 141 § eleven. different Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY vital GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .

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Mat. , 41 (5):270-278 (1966). 443. E. Kunz, Gruppenringe und Differentiale. Math. , 163(4):346-350 (1966). 444. H. Kupisch, Symmetrische Algebren mit endlich vielen unzerlegbaren Darstellungen. 1. J. reine und angew. , 219(1-2):1-25 (1965). 445. H. Kupisch,Ober Klasse von Ringen mit Minimalbedingung I. Arch. , 17(1):20-35 (1966). 446. Y. Kurata, On an additive ideal theory in a non-associative ring. Math. , 88(2):129-135 (1965). RING THEORY 45 447. J. P. Lafon, Spectre premierbilat~re de l'anneaux des endomorphismes d'un module de type fini.

Math. , 95(3): 212-222 (1967). 213. R. B. Brown, On generalized Cayley-Dickson algebra. Padf. J. , 20(3): 415-422 (1967). 214. R. H. Bruck, The algebra of dimension-linking operators. Canad. Math. , 8(2):203-222 (1965). 215. P. Burmeister and J. Schmidt, On the completion of partial algebras. Colloq. , 17(2):235-245 (1967). 216. R. G. Buschman, Quasi-inverses of sequences. Amer. Math. Monthly, 73(4):134135 (1966). 217. D. Butuc and M. Scutaru, Relatti si liirgirea notiunii de numilr. Gaz. mat. (RSR), A 72(10):370-378 (1967).

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. 25-36. V. I. Amautov, "Pseudonormalizability criterion for topological rings," Algebra Logika, Seminar, 4(4):3-24 (1965). V. I. Amautov, "Topologization of the ring of integers," Bu!. Akad. , No.

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