【摘 要】
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Let B be a ring with 1, p an automorphism of B of order n for some integer n, and B[x; p] the skew polynomial ring in x over B such that 1, x,x2,... ,xn-1 are i
【机 构】
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Department of Mathematics, Bradley University Peoria, Illinois 61625, USA E-mail: szeto@hilltop. bra
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Let B be a ring with 1, p an automorphism of B of order n for some integer n, and B[x; p] the skew polynomial ring in x over B such that 1, x,x2,... ,xn-1 are independent over B and xn ∈ U(Bp), where Bp is the set of elements in B fixed under p and U(Bρ) is the set of all units in Bρ. Let -ρ be the inner automorphism of B[x; p] induced by x. Assume n is a unit in B. It is shown that, for a -ρ-Galois extension B[x; p] over (B[x; ρ])-ρ (resp., a DeMeyer-Kanzaki Galois extention B over Bp), B[x; ρ] is Azumaya if and only if (B[x; ρ])-ρ (resp.,B) is Azumaya, and some splitting rings of B[x; ρ], (B[x; ρ])-ρ and B coincide.
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