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 includes 5 assessment 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 critical geometry and differential-geometric tools within the calculus of diversifications within the latter. The literature lined 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 class of earrings. . . . . . . . . . . . sixty six § four. Quasi-Frobenius jewelry and Their Generalizations. . seventy one § five. a few elements of Homological Algebra . . . . . . . . . . seventy five § 6. Endomorphism jewelry . . . . . . . . . . . . . . . . . . . . . eighty three § 7. different features. . . . . . . . . . . . . . . . . . . 87 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , ninety one LATTICE concept M. M. Glukhov, 1. V. Stelletskii, and T. S. Fofanova § 1. Boolean Algebras . . . . . . . . . . . . . . . . . . . . . " 111 § 2. identification and Defining family 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 features. . . . . . . . . . . . . . . . . . . . . . 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 crucial GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .

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Amer. Math. , 124(1):77-93 (1966). 361. D. B. Ion, Asupra algebrelor Jordan de tip A. Studii si cercetari mat. Acad. RPR, 17(2):301-310 (1965). 362. D. B. Ion, Asupra unor proprietli~i ale constantelor de structura ale algebrelor Jordan de tip A. Studii ~i cercetari mat. Acad. RPR, 19(7):1031-1038 (1967). 363. D. B. Ion, Asupra unor propriediti ale radacinilor algebrelor Jordan de tip A. Studii >si cercetari mat. Acad. RPR, 18(2):309-313 (1966). 364. 1. D. Ion, Radicalul limitei projective de inele asociative.

M. Turchin. " Mat. Zametki. 2(2):133-138 (1967). 28 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. L. A. BOKUT', K. A. ZHEVLAKOV,AND E. N. KUZ'MIN Z. M. Dyment, "Maximal commutative nilpotent subalgebra of a sixth-order matrix algebra," Vestsi A kad. Nauk BSSR, Ser. -Mat. 3, 53-68 (1966). V. P. Elizarov, "Plane extensions of rings," Dokl. Akad. Nauk SSSR, 175(4):759761 (1967). v. P. Elizarov, "Two properties of associative rings," Mat. Zametki, 2(3):225232 (1967).

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. Bull. Acad. polon. sci. Sec. sci. , astron.

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