Finiteness in projective ideals
نویسندگان
چکیده
منابع مشابه
ON FINITENESS OF PRIME IDEALS IN NORMED RINGS
In a commutative Noetherian local complex normed algebra which is complete in its M-adic metric there are only finitely many closed prime ideals.
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A theorem concerning some descriptive properties of σ-ideals and generalizing the main result of [1] is proved. Various applications of this theorem are also presented. 2000 Mathematics Subject Classification: 03E15, 28A05, 28B20.
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Throughout we let (T,m, k) denote a commutative Noetherian local ring with maximal ideal m and residue field k. We let I ⊆ T be an ideal generated by a regular sequence of length c and set R := T/I. In the important paper [A], Avramov addresses the following question. Given a finitely generated R-module M , when does M have finite projective dimension over a ring of the form T/J , where J is ge...
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We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. This family subsumes and improves upon constructions given in [Cav04] and [McC]. In particular, we describe a family of three-generated homogeneous ideals in arbitrary characteristic whose projective dimension grows
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For an ideal I in a polynomial ring over a field, a monomial support of I is the set of monomials that appear as terms in a set of minimal generators of I. Craig Huneke asked whether the size of a monomial support is a bound for the projective dimension of the ideal. We construct an example to show that, if the number of variables and the degrees of the generators are unspecified, the projectiv...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1973
ISSN: 0021-8693
DOI: 10.1016/0021-8693(73)90045-8