About the condition Going up to R subset of R

作者：Zoeschinger Helmut

来源：Archiv der Mathematik, 2010, 95(3): 225-231.

DOI：10.1007/s00013-010-0168-3

• Artinian modules and noetherian dimension
• Coattached primes
• Formal fibers
• Local cohomology

Let (R, m) be a noetherian, local ring with completion R. We show that R subset of R satisfies the condition Going up if and only if there exists to every artinian R-module M with Ann(R)( M) subset of p a submodule U subset of M with Ann(R)( U) = p. This is further equivalent to R being formal catenary, to alpha( R) = 0 and to H(q/p)(d)(R/p) = 0 for all prime ideals p subset of q not subset of m where d = dim( R/ p).

• 出版日期2010-9