Newtonian valued differential fields with arbitrary value group

Maximal Immediate Extensions of Valued Differential Fields

We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an extension.

On the Valued Function Fields with given Value Group and Residue Field or with given Residue Field and Genus

The valued function fields with given value group and residue field or with given genus and residue field are studied.

Differential Calculus, Manifolds and Lie Groups over Arbitrary Infinite Fields

We present an axiomatic approach to finiteand infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed. Special attention is paid to the case of mappings between topological vector spaces over non-discrete topological fields, in particular ultrametric fields or the fie...

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.

Amalgamating valued fields