Rings with two-generated ideals
نویسندگان
چکیده
منابع مشابه
Countably Generated Ideals in Rings of Continuous Functions
1. Results. Scattered results about countably2 generated ideals in C(X) are established in [2] and [4] : Op is countably generated if and only if pEX and p has a countable base of neighborhoods; Op is both prime and countably generated if and only if Mp is principal, and if and only if pEX and p is isolated; no lower prime ideal is countably generated. We generalize these as follows: if Mp is c...
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The aim of this paper is to study jumping numbers and multiplier ideals of any ideal in a two-dimensional local ring with a rational singularity. In particular we reveal which information encoded in a multiplier ideal determines the next jumping number. This leads to an algorithm to compute sequentially the jumping numbers and the whole chain of multiplier ideals in any desired range. As a cons...
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We show that in a local S1 ring every two-generated ideal of linear type can be generated by a two-element sequence of linear type and give an example which illustrates that the S1 condition is essential. We also show that every Noetherian local ring in which every two-element sequence is of linear type is an integrally closed integral domain and every two-generated ideal of it can be generated...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1991
ISSN: 0022-4049
DOI: 10.1016/0022-4049(91)90032-w