On Galois theory using pencils of higher derivations

Pencils of Higher Derivations of Arbitrary Field Extensions

Let L be a field of characteristic p ^ 0. A subfield K of L is Galois if A' is the field of constants of a group of pencils of higher derivations on L. Let F d K be Galois subfields of L. Then the group of L over F is a normal subgroup of the group of L over K if and only if F = K(W') for some nonnegative integer r. If L/K splits as the tensor product of a purely inseparable extension and a sep...

Local higher derivations on C*-algebras are higher derivations

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

Higher Derivations in Invariant Theory

Much of the wonderful invariant theory of the 19 century worked over fields of characteristic zero, while the theory for prime characteristic lagged behind. However, the Frobenius (p power) map in characteristic p > 0 leads to a rich theory of invariants in prime characteristic. This theory is closely bound up with the Steenrod Algebra, which allows us to derive new invariants from known invari...

Prime Higher Derivations on Algebras

HIGHER DERrVATION GALOIS THEORY OF FIELDS

A Galois correspondence for finitely generated field extensions k/h is presented in the case characteristic h = p ^ 0. A field extension k/h is Galois if it is modular and h is separably algebraically closed in k. Galois groups are the direct limit of groups of higher derivations having rank a power of p. Galois groups are characterized in terms of abelian iterative generating sets in a manner ...