Bimodules, the Brauer group, Morita equivalence, and cohomology
For \(k\)-algebras \(A\) and \(B\) let \(A\)-mod-\(B\) denote the category of \((A\)- \(B)\)-bimodules. A \(k\)-linear equivalence of categories \(A: A\)-mod-\(A\to B\)-mod-\(B\) is called a (weak) \(k\)-congruence if \(TA\approx B\). The author shows that many familiar Morita invariant properties (e.g. the Hochschild and cyclic cohomologies, the center) are trivially seen to be congruence invariant. The congruence is used to give an economical description of the Brauer group and to answer \textit{D. Zelinsky's} concluding question [in: Ring Theory II, Proc. 2nd Okla. Conf. 1975, 69-101 (1977; Zbl 0356.13002)].
scientific article; zbMATH DE number 89588
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