2007/05/09 by Pramod Kumar Sharma, Sharma, Pramod K.
Mathematics · #13A15 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.0705.1286
openalex publication_date 2007/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the notion of a power stable ideal in a polynomial ring R[X] over an integral domain R . It is proved that a maximal ideal χ M in R[X] is power stable if and only if Pt is P- primary for all t≥ 1 for the prime ideal P = M ∩ R . Using this we prove that for a Hilbert domain R any radical ideal in R[X] which is a finite intersection G-ideals is power stable. Further, we prove that if R is a Noetherian integral domain of dimension 1 then any radical ideal in R[X] is power stable. Finally, it is proved that if every ideal in R[X] is power stable then R is a field.