Correspondences between Valued Division Algebras and Graded Division Algebras
نویسنده
چکیده
If D is a tame central division algebra over a Henselian valued field F , then the valuation on D yields an associated graded ring GD which is a graded division ring and is also central and graded simple over GF . After proving some properties of graded central simple algebras over a graded field (including a cohomological characterization of its graded Brauer group), it is proved that the map [D] [GD]g yields an index-preserving isomorphism from the tame part of the Brauer group of F to the graded Brauer group of GF . This isomorphism is shown to be functorial with respect to field extensions and corestrictions, and using this it is shown that there is a correspondence between F -subalgebras of D (with center tame over F ) and graded GF -subalgebras of GD.
منابع مشابه
Nondegenerate semiramified valued and graded division algebras
In this paper, we define what we call (non)degenerate valued and graded division algebras [Definition 3.1] and use them to give examples of division p-algebras that are not tensor product of cyclic algebras [Corollary 3.17] and examples of indecomposable division algebras of prime exponent [Theorem 5.2, Corollary 5.3 and Remark 5.5]. We give also, many results concerning subfields of these divi...
متن کاملOn normalizers of maximal subfields of division algebras
Here, we investigate a conjecture posed by Amiri and Ariannejad claiming that if every maximal subfield of a division ring $D$ has trivial normalizer, then $D$ is commutative. Using Amitsur classification of finite subgroups of division rings, it is essentially shown that if $D$ is finite dimensional over its center then it contains a maximal subfield with non-trivial normalize...
متن کاملWeighted composition operators between Lipschitz algebras of complex-valued bounded functions
In this paper, we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces, not necessarily compact. We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators. We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.
متن کاملNicely semiramified division algebras over Henselian fields
We recall that a nicely semiramified division algebra is defined to be a defectless finitedimensional valued central division algebra D over a field E with inertial and totally ramified radical-type (TRRT) maximal subfields [7, Definition, page 149]. Equivalent statements to this definition were given in [7, Theorem 4.4] when the field E is Henselian. These division algebras, as claimed in [7, ...
متن کامل