## Show that if the nucleus of two distributions is the same, then one is a constant multiple of the other.

If the set of test functions corresponding to the distribution core f coincides with the distribution core g, then the distribution f is a constant multiple of g.

## nt.number theory – Calculation of the nucleus of a vector space using fixed field automorphisms of field

Leave $$E$$ be a vector space on the field $$K$$, where $$K$$ is a numeric field (finite extension of $$mathbb {Q}$$) To consider $$Fix_K ( phi)$$ as the fixed field of automorphism $$phi$$. Is it possible to calculate the core of the vector space? $$E$$ using $$Fix_K$$ or is there any relation of $$Fix_K$$ to the $$Ker (E)$$?

## Nucleus of the determining morphism of the first algebraic K theory

Yes $$A$$ is the coordinate ring of a uniform variety over a finite field, it is known if the core of the determinant map $$K_1 (A) rightarrow A ^ { times}$$ Is it torsion or not?