By S. A. Amitsur (auth.), Freddy M. J. van Oystaeyen, Alain H. M. J. Verschoren (eds.)

**Read or Download Brauer Groups in Ring Theory and Algebraic Geometry: Proceedings, University of Antwerp U.I.A., Belgium, August 17â€“28, 1981 PDF**

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**Extra resources for Brauer Groups in Ring Theory and Algebraic Geometry: Proceedings, University of Antwerp U.I.A., Belgium, August 17â€“28, 1981**

**Sample text**

Then Brg (C) - Brg (C/~0. 2. Let's show that it is also surjective. , H 2 (r~,U(S)) ~ H~ (~,, U (S/~O). 5. It follows that Ker deg2R = Ker deg2R/~, and the desired result follows from ~neorem 2. I0. 42 References I M. Auslander, B. Goldman,The Brauer ~roup of a Commutative Rin? Trans. Am. ~gth. Soc. 97 (1960), 367-407. 2 F. Demeyer, E. In2raham, Separable Algebras over Commutative Rings Lect. Notes in Math. 181, Springer Verlag ]970. 3 J. Kelley, General ToDoloFy , Van Nostrand, New York, 1955.

V n w i t h and dn > ... > d I. (this is possible if one all~vs some deg u i = di,deg vi=-d i of the ui, v i to be zero). u for j = I, j n ... i-~ with i < n, hence d i < c~n. e. the non-zero contributions in the s u m @ p e a r with k < i. If we multiply this relation, by UnV i we ob- tain (UnVi)2 = 0. n, all s ~ S. ) : u _1 = c ] O _1 v w i t h c U,U _i ~ U)U U (S). n. n, co~nutes with S. v. n. Since S semiprime (UnVj) 2 = 0 implies UnV i = O. By completely symmetric argumentation (using ] = vu) we find viu n = 0 too.

249-300. [4] A. " [5] P. " Math. Ann. 150 (1963), pp. 411-439. [6] P. " Jour. Mathematik 214/215 (1964), pp. 207-226. [7] D. " [8] E. " pp. 12-28. Hebrew University and Yale University Ann. Math. Ann. Ecole Comm. Alg. 6 (1978), pp. 1017-1035. J. Alg. 7 (1979), pp. 333-345. Mat. Zeit. 39 (1934), CROSSED PRODUCTS OVER GRADED LOCAL RINGS S. , Belgium F. , Belgium 0. Introduction In the theory of the Brauer group of a commutative rinp, local rings present a very nice case because every Azu~aya alpebra over a Iocal tiny is equivalent On the Brauer group sens@ to a crossed product algebra.