The closed socle of a relative Azumaya algebra
In [Lect. Notes Math. 917, 260-278 (1982; Zbl 0484.16002)], the author introduced the notion of a relative Azumaya algebra with respect to an idempotent kernel functor and applied it to the study of the Brauer group of a quasi-affine scheme. In this paper, the notion of closed socle of an Azumaya algebra introduced by \textit{D. E. Haile} [J. Algebra 51, 97-106 (1978; Zbl 0375.16004)] (see also [\textit{F. R. DeMeyer}, Proc. Am. Math. Soc. 78, 299-303 (1980; Zbl 0435.13001)]) is extended to relative Azumaya algebras. The notion is Brauer invariant (in the relative sense) and yields information about the splitting of relative Azumaya algebras. Some geometrical applications are given.
scientific article; zbMATH DE number 3842066
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