The corestriction of valued division algebras over Henselian fields. I

Kummer subfields of tame division algebras over Henselian valued fields

By generalizing the method used by Tignol and Amitsur in [TA85], we determine necessary and sufficient conditions for an arbitrary tame central division algebra D over a Henselian valued field E to have Kummer subfields [Corollary 2.11 and Corollary 2.12]. We prove also that if D is a tame semiramified division algebra of prime power degree p over E such that p 6= char(Ē) and rk(ΓD/ΓF ) ≥ 3 [re...

Nicely 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, ...

Triangulaizability of Algebras Over Division Rings

An Isomorphism Theorem for Henselian Algebraic Extensions of Valued Fields

In general, the value groups and the residue elds do not suuce to classify the algebraic henselian extensions of a valued eld K, up to isomorphism over K. We deene a stronger, yet natural structure which carries information about additive and multiplica-tive congruences in the valued eld, extending the information carried by value groups and residue elds. We discuss the cases where these \mixed...

FUZZY HYPERVECTOR SPACES OVER VALUED FIELDS

In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.