In this paper we consider test polynomials in the polynomial algebra and the free associative algebra. A test polynomial is defined by the following property: every endomorphism which fixes the polynomial is an automorphism. We construct families of test polynomials for the polynomial algebra and th
New classes of test polynomials of polynomial algebras
โ Scribed by Keqin Feng; Jietai Yu
- Publisher
- SP Science China Press
- Year
- 1999
- Tongue
- English
- Weight
- 421 KB
- Volume
- 42
- Category
- Article
- ISSN
- 1674-7283
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Some preliminaries In this section we define some of the terms used in the paper and state some results for later use. All rings considered in this paper are commutative and Noetherian and all modules considered are assumed to be finitely generated. For a module M over a ring, ยต(M) will denote t
Let K X Y = K x 1 x n y 1 y m be the polynomial algebra in m + n variables over a field K of characteristic 0. Let ฮด be a locally nilpotent derivation of K X Y such that ฮด y i = 0, i = 1 m, and let ฮด act as a K Y -affine transformation over the free K Y -module freely generated by x 1 x n . We pro
Let T be the generic trace algebra generated by the algebra R of two generic 2 = 2 matrices and by all traces of the matrices from R over a field K. We construct new automorphisms of T and R. They induce automorphisms of the polynomial algebra in five variables which fix two of the variables. Our au