# Quasi-linearity of cyclic monomial automorphisms

- Authors
- Journal
- Journal of Algebra 0021-8693
- Publisher
- Elsevier
- Publication Date
- Volume
- 95
- Issue
- 2
- Identifiers
- DOI: 10.1016/0021-8693(85)90118-8

## Abstract

Let K 1, K 2 be purely transcendental extensions of k of finite transcendence degrees and let s 1, s 2 be k-automorphisms of K 1, K 2 of finite orders. In Theorem 1.5, it is shown that if s 1 acts linearly (on some base of K 1) and if order( s 1) divides order( s 2), then s 1 ⊛ s 2 is (quasi-) equivalent to I ⊛ s 2, where I is the identity automorphism of K 1 and where s 1 ⊛ s 2 is the k-automorphism induced by s 1 and s 2 on the quotient field K 1 ⊛ K 2 of K 1 ⊗ k K 2. This fact and results from [1] are then used to prove that every cyclic monomial automorphism is quasilinearizable (Theorem 2.5).

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