نتایج جستجو برای: noetherian dimension

تعداد نتایج: 113264  

2006
Daniel Murfet

Recall that a regular local ring is a noetherian local ring with dimension equal to dimkm/m. A regular local ring of dimension one is precisely a discrete valuation ring. If V is a nosingular variety then t(V ) is a scheme with all local rings regular, so t(V ) is clearly regular in codimension one. In this section we will consider schemes satisfying the following condition: (∗) X is a noetheri...

2009
B. Olberding

The class of Matlis domain, those integral domains whose quotient field has projective dimension 1, is surprisingly broad. However, whether every domain of Krull dimension 1 is a Matlis domain does not appear to have been resolved in the literature. In this note we construct a class of examples of one-dimensional domains (in fact, almost Dedekind domains) that are overrings of K[X, Y ] but are ...

2009
Rafael Parra

Given a significative class F of commutative rings, we study the precise conditions under which a commutative ring R has an F -envelope. A full answer is obtained when F is the class of fields, semisimple commutative rings or integral domains. When F is the class of Noetherian rings, we give a full answer when the Krull dimension of R is zero and when the envelope is required to be epimorphic. ...

2009
DIANA WHITE

We introduce and investigate the notion of GC -projective modules over (possibly non-noetherian) commutative rings, where C is a semidualizing module. This extends Holm and Jørgensen’s notion of C-Gorenstein projective modules to the non-noetherian setting and generalizes projective and Gorenstein projective modules within this setting. We then study the resulting modules of finite GC-projectiv...

‎It is shown that‎ ‎if $M$ is an Artinian module over a ring‎ ‎$R$‎, ‎then $M$ has Noetherian dimension $alpha $‎, ‎where $alpha $ is a countable ordinal number‎, ‎if and only if $omega ^{alpha }+2leq it{l}(M)leq omega ^{alpha‎ +1}$, ‎where $ it{l}(M)$ is‎ ‎the length of $M$‎, ‎$i.e.,$ the least ordinal number such that the interval $[0‎, ‎ it{l}(M))$ cannot be embedded in the lattice of all su...

2009
ALINA IACOB SRIKANTH B. IYENGAR S. B. IYENGAR

A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast the problem on hand into one about the homotopy category of complexes of injective modules. Analogous results for flat dimension and projective dimension are also established.

Journal: :Journal of Pure and Applied Algebra 1988

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