Prime ideals in differential operator rings. Catenarity
نویسندگان
چکیده
منابع مشابه
Localization and Catenarity in Iterated Differential Operator Rings
Let k be a field, R an associative k-algebra with identity, a finite set of derivations of R, and R 1 1 · · · n n an iterated differential operator k-algebra over R such that j i ∈ R 1 1 · · · i−1 i−1 1 ≤ i < j ≤ n. If R is Noetherian -hypercentral, then every prime ideal P of A is classically localizable. The aim of this article is to show that under some additional hypotheses on the -prime id...
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The ideal I 1 generated by the 2 2 quantum minors in the coordinate algebra of quantum matrices, O q (M m;n (k)), is investigated. Analogues of the First and Second Fundamental Theorems of Invariant Theory are proved. In particular, it is shown that I 1 is a completely prime ideal, that is, O q (M m;n (k))=I 1 is an integral domain, and that O q (M m;n (k))=I 1 is the ring of coinvariants of a ...
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In this paper, it has been proved that for a Noetherian ring R and an automorphism σ of R, an associated prime ideal of R[x, σ] or R[x, x−1, σ] is the extension of its contraction to R and this contraction is the intersection of the orbit under σ of some associated prime ideal of R. The same statement is true for minimal prime ideals also. It has also been proved that for a Noetherian Q-algebra...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1990
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1990-0946215-3