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New from MARCEL DEIUKER, Inc. 270 Msdison Avenue, New York, N. Y. 10016 B r a u e r G r o u p s a n d t h e C o h o m o l o g y of G r a d e d R i n g s . (Pam and Applied Mathematics: A Series of Monographs and Textbooks/l21.) By Stefaan CAENEPEEL and Freddy van OYSTAEYEI. 1988.280 pages, bound, illustrated. $ 89.75 (U.S. and Can&); $ 107.50 (All other countries). ISBN: 0-8247-7978-9. (Prices subject to change without notice.) B r a u e r G r o u p s a n d t h e C o h o m o l o g y o f G r a d e d R i n g s provides acompleteanalysisof its subject. It uses Galois, Amitsur, and etale cohomological methods as well as a cohomology on suitably chosen sites, applying them to gradations by finite groups. In this way, these new methods yield new facts concerning the Brauer-Wall and Braner-Long groups.
Illustrated with 44 diagrams, this informative reference provides a unique source for an algebraic approach to etale cohomology, Verdier coverings, convergence of Cech cohomology, and other techniques . . . gives a counterexample to the graded version of Artin's theorem but shows the theorem remains valid if restricted to rings strongly graded on the etale site . . . draws a connection with generalized crossed products useful when phrasing crossed product structure theorems over ground rings having a nontrivial Picard group . . . and more.
Readership: Algebraists, ring theorists, and graduato mathematics students.