We gather some basic facts concerning
algebra endomorphisms of
Weyl algebras for fields with
positive characteristic .
These facts could lead some preliminary results on Dixmier conjecture.

**Yoshifumi Tsuchimoto **

*(To appear in Mem. Fac. Sci. Kochi Univ. (Math.) 24
(2003))*

Key words and phrases: Jacobian conjecture, Dixmier conjecture, Noncommutative algebra

1991 Mathematics Subject Classification: 14R15(16W20)

- Contents
- Introduction
- Notations

- First properties of Weyl algebras
- reduction to characteristic
- Weyl algebras over fields of positive characteristics and their centers
- Algebra endomorphisms and centers of Weyl algebras
- A splitting algebra of
- The quotient field of the Weyl algebra
- definition of reduced trace and reduced norm
- Algebra endomorphism and splitting of Weyl algebra
- the geometric degree
- uniqueness of an operator -th root for generators of
- Algebra endomorphisms of Weyl algebras are determined by its restriction to the center

- Reduced trace and reduced norm

- injectivity ()

- multidegree monoids and lattices

- Bibliography
- About this document ...

2003/3/3