Normalized Brauer factor sets

[摘要] We investigate normalized Brauer factor sets of central simple algebras with respect to arbitrary maximal separable subalgebras, and show that they have a cohomological description. As a consequence, a central simple algebra of even degree having a normalized Brauer factor set cannot be a division algebra. An intrinsic equivalent condition is given for a central simple algebra to have a normalized Brauer factor set. Consequently, an algebra has a normalized Brauer factor set if it is a square in the relative Brauer group, The converse holds for index 4, or for symbols, but an example is given of an algebra of index 8 with normalized Brauer factor set, which is not a square in the relative Brauer group. On the ether hand, suppose D is a division algebra of odd degree. If D has a maximal separable subfield K whose Galois group G satisfies a certain property (which automatically holds for \G\ odd) then D contains an element a for which tr[a] = tr a(2) = tr a(-1) = 0. (C) 1997 Academic Press.

[发布日期] 1997-12-15