Constants of algebraic derivativations

A téma kiírójának neve és tanszéke: 
Hegedüs Pál, Algebra Tanszék
A téma kiírójának e-mail címe: 
hegpal@math.bme.hu
Típus: 
TDK téma
Szakdolgozat téma
Diplomamunka téma
PhD téma

Derivativations of a ring R are additive f:RR functions for which f(rs)=rf(s)+f(r)s. An element rR is a constant of f if f(r)=0. It is clear that they form a subring. We study the derivativations of n-variable polynomal algebras over a field. We are interested in which properties of the derivation are reflected by the properties of the algebra of constants.

 

For a BSc thesis we expect a survey of the important results in a simple aspect of the problem.

For a MSc thesis we expect a fuller survey and a discussion of underlying interconnections.

For a TDK submission we expect the solution of a special case.

For a PhD thesis we expect the solution of several cases or a radically new reinterpretation of a broad area.