On Power Stable Ideals
نویسنده
چکیده
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 P t 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.
منابع مشابه
On Some Partial Orders Associated to Generic Initial Ideals
We study two partial orders on [x1, . . . , xn], the free abelian monoid on {x1, . . . , xn}. These partial orders, which we call the “strongly stable” and the “stable” partial order, are defined by the property that their filters are precisely the strongly stable and the stable monoid ideals. These ideals arise in the study of generic initial ideals.
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