Semiorderings and stability index under field extensions

Differential Forms and Bilinear Forms under Field Extensions

Let F be a field of characteristic p > 0. Let Ω(F ) be the F vector space of n-differentials of F over F . Let K = F (g) be the function field of an irreducible polynomial g in m > 1 variables over F . We derive an explicit description of the kernel of the restriction map Ω(F ) → Ω(K). As an application in the case p = 2, we determine the kernel of the restriction map when passing from the Witt...

Estimating stability and selection index

On stability of the hamiltonian index under contractions and closures

The hamiltonian index of a graph G is the smallest integer k such that the k th iterated line graph of G is hamiltonian We rst show that with one exceptional case adding an edge to a graph cannot increase its hamiltonian index We use this result to prove that neither the contraction of an AG F contractible subgraph F of a graph G nor the closure operation performed on G if G is claw free a ects...

Higher Derivations and Field Extensions

Let K be a field having prime characteristic p. The following conditions on a subfield k of K are equivalent: (i) || K" (k) = k and K/k is separable, (ii) k is the field of constants of an infinite higher derivation defined in K. (iii) k is the field of constants of a set of infinite higher derivations defined in K. If K/k is separably generated and k is algebraically closed in K, then k is the...

NORMAL FIELD EXTENSIONS Kjk AND

Throughout the paper Kjk is a field extension and p is the exponent characteristic. In this paper I introduce the notion of .K/fc-bialgebra (coalgebra over K and algebra over k) and describe a theory of finite dimensional normal field extensions Kjk based on a ^-measuring A /̂A:-bialgebra H(Kjk) (see 1.2, 1.6 and 1.10). This approach to studying Kjk was inspired by my conviction that a successfu...