On a generalization of the principal ideal theorem
نویسندگان
چکیده
منابع مشابه
GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES
The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.
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KrulΓs principal ideal theorm [Krull] states that q elements in the maximal ideal of a local noetherian ring generate an ideal whose minimal components are all of height at most q. Writing R for the ring, we may consider the q elements, x19 , xq say, as coordinates of an element xeR. It is an easy observation that every homomorphism R —> R carries x to an element of the ideal generated by xi9 ,...
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In the p-th cyclotomic field Qpn , p a prime number, n ∈ N, the prime p is totally ramified and the only ideal above p is generated by ωn = ζpn − 1, with the primitive p-th root of unity ζpn = e 2πi pn . Moreover these numbers represent a norm coherent set, i.e. NQpn+1/Qpn(ωn+1) = ωn. It is the aim of this article to establish a similar result for the ray class field Kpn of conductor p over an ...
متن کاملgeneralized principal ideal theorem for modules
the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1950
ISSN: 0040-8735
DOI: 10.2748/tmj/1178245697