期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2007
卷号：2007
DOI：10.1155/2007/20138
出版社：Hindawi Publishing Corporation
摘要：Let R
be a ring. Let σ be an automorphism of R. We define a
σ-divided ring and prove the following.
(1) Let R be a commutative pseudovaluation ring such that x∉P for any
P∈Spec(R[x,σ])
. Then R[x,σ] is also a pseudovaluation ring.
(2) Let R be a σ-divided ring such that x∉P for any
P∈Spec(R[x,σ]).
Then R[x,σ] is also a σ-divided ring.
Let now R be a commutative Noetherian Q-algebra (Q is the field of rational
numbers). Let δ be a derivation of R. Then we prove the following.
(1) Let R be a commutative pseudovaluation ring. Then R[x,δ] is also a
pseudovaluation ring.
(2) Let R be a divided ring. Then R[x,δ] is also a divided ring.
