In a previous article (J. Algebra 367 (2012), 142-165) we established axiomatic parametrised Cohen-Macaulay approximation which in particular was applied to pairs consisting of finite type flat family rings and modules. this sequel study the induced maps deformation functors deduce properties like smoothness injectivity under general, mainly cohomological conditions on module.

Let (R, m) be a Noetherian local ring and let I be an R-ideal. Inspired by the work of Hübl and Huneke, we look for conditions that guarantee the Cohen-Macaulayness of the special fiber ring F = R/mR of I, where R denotes the Rees algebra of I. Our key idea is to require ‘good’ intersection properties as well as ‘few’ homogeneous generating relations in low degrees. In particular, if I is a str...

Let $(R,m)$ be a commutative Noetherian local ring, $M$ a finitely generated $R$-module of dimension $d$, and let $I$ be an ideal of definition for $M$. In this paper, we extend cite[Corollary 10(4)]{P} and also we show that if $M$ is a Cohen-Macaulay $R$-module and $d=2$, then $lambda(frac{widetilde{I^nM}}{Jwidetilde{I^{n-1}M}})$ does not depend on $J$ for all $ngeq 1$, where $J$ is a minimal ...

To reduce to resolving Cohen–Macaulay singularities, Faltings initiated the program of “Macaulayfying” a given Noetherian scheme X. For wide class X, Kawasaki built sought-for modifications, with crucial drawback that his blowups did not preserve locus CM(X)?X, where X is already Cohen–Macaulay. We extend Kawasaki’s methods show every quasi-excellent, has X˜ proper map X˜?X an isomorphism over ...

Abstract In this paper, we characterize homogeneous arithmetically Cohen–Macaulay (ACM) bundles over isotropic Grassmannians of types

We prove that certain class of Stanley–Reisner rings having sufficiently large multiplicities are Cohen–Macaulay using Alexander duality.