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 includes 5 overview articles, 3 within the Al­ gebra half and within the Geometry half, surveying the fields of ring concept, modules, and lattice concept within the former, and people of essential geometry and differential-geometric tools 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', okay. 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 jewelry. . . . . . . . . . . . sixty six § four. Quasi-Frobenius jewelry and Their Generalizations. . seventy one § five. a few facets 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 kinfolk in Lattices . . . . . . one hundred twenty § three. Distributive Lattices. . . . . . . . . . . . . . . . . . . . . 122 vii viii CONTENTS § four. Geometrical elements 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 on. . . . . . . . . 134 § eight. Closure Operators . . . . . . . . . . . . . . . . . . . . . . . 136 § nine. Topological elements. . . . . . . . . . . . . . . . . . . . . . 137 § 10. Partially-Ordered units. . . . . . . . . . . . . . . . . . . . 141 § eleven. different Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY vital GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .

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M. Djabali, Anneau de fractions d'un J-anneau. Semin. Dubreil et Pisot Fac. Sci. Paris, 18(1):8/01-8/12 (1967). 257. M. Djabali, Demi-groupes nilpotents et radical d'un anneau noetherien ou artinien. C. r. Acad. , 264(1l:A493-A495 (1967). RING THEORY 37 258. F. Drollinger, Ober die Struktur nilpotenter und auflosbarer Liescher Algebren. Comment. math. , 42(4):259-284 (1967). 259. D. Dubois, Modules of sequences of elements of a ring. J. London Math. , 41(1):177-180 (1966). 260. D. Dubois, A note on David Harrison's theory of preprimes.

19(1):205-208 (1968). 421. K. Koh, On very large one-sided ideals of a ring. Canad. Math. , 9(2): 191-196 (1966). 422. K. Koh, On simple rings with maximal annihilator right ideals. Canad. Math. , 8 (5):667 -668 (1965). 44 1. A. BOKUT', K. A. ZHEVLAKOV, AND E. N. KUZ'MIN 423. K. Koh, A note on a certain class of prime rings. Amer. Math. Monthly, 72(1): 46-48 (1965). 424. K. Koh, On the class of rings which do not contain nonzero semi-singular ideals. Amer. Math. Monthly, 72(8):875-877 (1965).

Hirsch, A note on non-commutative polynomial rings subject to degreepreservation. J. London Math. , 42(2J:3311-335 (196'7). 346. G. Hochschild. An addition to Ado's theorem. Proc. Amer. Math. , 17(2): 531-533 (1966). 347. P. Holgate, Sequences of powers in genetic algebras. J. London Math. , 42(3): 489-496 (1967). 348. P. Holgate, Genetic algebras associated with polyploidy. Proc. Edinburgh Math. , 15(0:1-9 (1966). 349. P. Holgate, The genetic algebra k linked loci. Proc. London Math. , 18(3): 315-327 (1968).

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