A characterization of closure operations that induce big Cohen-Macaulay modules
نویسندگان
چکیده
منابع مشابه
Lefschetz Extensions, Tight Closure, and Big Cohen-macaulay Algebras
We associate to every equicharacteristic zero Noetherian local ring R a faithfully flat ring extension which is an ultraproduct of rings of various prime characteristics, in a weakly functorial way. Since such ultraproducts carry naturally a non-standard Frobenius, we can define a new tight closure operation on R by mimicking the positive characteristic functional definition of tight closure. T...
متن کاملLiaison with Cohen–Macaulay modules
We describe some recent work concerning Gorenstein liaison of codimension two subschemes of a projective variety. Applications make use of the algebraic theory of maximal Cohen–Macaulay modules, which we review in an Appendix.
متن کاملA characterization of shellable and sequentially Cohen-Macaulay
We consider a class of hypergraphs called hypercycles and we show that a hypercycle $C_n^{d,alpha}$ is shellable or sequentially the Cohen--Macaulay if and only if $nin{3,5}$. Also, we characterize Cohen--Macaulay hypercycles. These results are hypergraph versions of results proved for cycles in graphs.
متن کاملRESULTS ON ALMOST COHEN-MACAULAY MODULES
Let $(R,underline{m})$ be a commutative Noetherian local ring and $M$ be a non-zero finitely generated $R$-module. We show that if $R$ is almost Cohen-Macaulay and $M$ is perfect with finite projective dimension, then $M$ is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient condition on $M$ to be an almost Cohen-Macaulay module, by using $Ext$ functors.
متن کاملIndecomposable Cohen-macaulay Modules and Their Multiplicities
The main aim of this paper is to find a large class of rings for which there are indecomposable maximal Cohen-Macaulay modules of arbitrary high multiplicity (or rank in the case of domains).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10417-3