Polynomial Rings over Pseudovaluation Rings

V. K. Bhat

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-6

Abstract:

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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:020138

DOI: 10.1155/2007/20138

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