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

This quantity includes 5 evaluate articles, 3 within the Al­ gebra half and within the Geometry half, surveying the fields of ring thought, modules, and lattice conception within the former, and people of necessary geometry and differential-geometric equipment within the calculus of diversifications within the latter. The literature lined is basically that released in 1965-1968. v CONTENTS ALGEBRA RING conception L. A. Bokut', ok. A. Zhevlakov, and E. N. Kuz'min § 1. Associative jewelry. . . . . . . . . . . . . . . . . . . . three § 2. Lie Algebras and Their Generalizations. . . . . . . thirteen ~ three. substitute and Jordan earrings. . . . . . . . . . . . . . . . 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 class of jewelry. . . . . . . . . . . . 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 facets. . . . . . . . . . . . . . . . . . . 87 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , ninety one LATTICE idea M. M. Glukhov, 1. V. Stelletskii, and T. S. Fofanova § 1. Boolean Algebras . . . . . . . . . . . . . . . . . . . . . " 111 § 2. identification and Defining family members in Lattices . . . . . . one hundred twenty § three. Distributive Lattices. . . . . . . . . . . . . . . . . . . . . 122 vii viii CONTENTS § four. Geometrical facets 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 on. . . . . . . . . 134 § eight. Closure Operators . . . . . . . . . . . . . . . . . . . . . . . 136 § nine. Topological points. . . . . . . . . . . . . . . . . . . . . . 137 § 10. Partially-Ordered units. . . . . . . . . . . . . . . . . . . . 141 § eleven. different Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY critical GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .

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Colo. , Dissert. , 26(1l):6736 (1966). 264. S. Elliger, Ober das Rangproblem bei Korpererweitrungen. J. reine und angew. , 221:162-175 (1966). 265. S. Elliger, Ober galoissche Korpererweiterungen von unendlichem Rang. Math. , 163(4):359-361 (1966). 266. S. Elliger, Konstruktion einfacher Ringe tiber einem einfachen Ring. Math. , 176(1):15-27 (1968). 267. Endliche Gruppen und Liesche Ringe, Ber. 12-18. 65. Math. Forschungsinst. Oberwolfach (1965), 9 pp. 268. M. Endo, On the topologies of the rational number field.

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Math. , 111(3):482-492 (1964). 439. E. Kreindler, Operateurs additifs dans les modules unitares a base denombrable. Bull. math. Soc. sci. math. RSR. 9(4):333-336 (1965). 440. I. L. Krivine, Anneaux preordonnes. I. , 12:307-326 (1964). 441. R. L. Kruse, "Rings with periodic additive group in which all subrings are ideal, " Doctoral dissertation, Calif. Inst. Technol. ; Dissert. Abstr. 25(8): 4725 (1965). 442. E. G. Kundert, Structure theory in s-d-rings. Atti Accad. naz, Lincei Rend. Cl. sci. , mat.

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