Quasi-linearity of cyclic monomial automorphisms

LetK1,K2 be purely transcendental extensions ofk of finite transcendence degrees and lets1,s2 bek-automorphisms ofK1,K2 of finite orders. In Theorem 1.5, it is shown that ifs1 acts linearly (on some base ofK1) and if order(s1) divides order(s2), thens1 ⊛ s2 is (quasi-) equivalent toI ⊛ s2, whereI is the identity automorphism ofK1 and wheres1 ⊛ s2 is thek-automorphism induced bys1 ands2 on the quotient fieldK1 ⊛ K2 ofK1 ⊗k K2. This fact and results from [1] are then used to prove that every cyclic monomial automorphism is quasilinearizable (Theorem 2.5)