Polynomial Rings over Pseudovaluation Rings

Autor: V. K. Bhat
Jazyk: angličtina
Rok vydání: 2007
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 2007 (2007)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
DOI: 10.1155/2007/20138
Popis: 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.
Databáze: Directory of Open Access Journals
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