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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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