Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence
112
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Let R be a local ring and C a semidualizing module of R. We investigate the behavior of certain classes of generalized Cohen-Macaulay R-modules under the Foxby equivalence between the Auslander and Bass classes with respect to C. In particular, we show that generalized Cohen-Macaulay R-modules are invariant under this equivalence and if M is a finitely generated R-module in the Auslander class with respect to C such that Cotimes_RM is surjective Buchsbaum, then M is also surjective Buchsbaum.
rate research
Read More
As a stable analogue of degenerations, we introduce the notion of stable degenerations for Cohen-Macaulay modules over a Gorenstein local algebra. We shall give several necessary and/or sufficient conditions for the stable degeneration. These conditions will be helpful to see when a Cohen-Macaulay module degenerates to another.
Let $(A,mathfrak{m})$ be a hypersurface ring with dimension $d$, and $M$ a MCM $A-$module with reduction no.2 and $mu(M)=2$ or $3$ then we have proved that depth$G(M)geq d-mu(M)+1$. If $e(A)=3$ and $mu(M)=4$ then in this case we have proved that depth$G(M)geq d-3$. When $A = Q/(f)$ where $Q = k[[X_1,cdots, X_{d+1}]]$ then we give estimates for depth $G(M)$ in terms of minimal presentation of $M$. Our paper is the first systematic study of depth of associated graded modules of MCM modules over hypersurface rings.
For a wide class of Cohen--Macaulay modules over the local ring of the plane curve singularity of type T_44 we explicitly describe the corresponding matrix factorizations. The calculations are based on the technique of matrix problems, in particular, representations of bunches of chains.
Let $A$ and $B$ be commutative rings with unity, $f:Ato B$ a ring homomorphism and $J$ an ideal of $B$. Then the subring $Abowtie^fJ:={(a,f(a)+j)|ain A$ and $jin J}$ of $Atimes B$ is called the amalgamation of $A$ with $B$ along $J$ with respect to $f$. In this paper, we study the property of Cohen-Macaulay in the sense of ideals which was introduced by Asgharzadeh and Tousi, a general notion of the usual Cohen-Macaulay property (in the Noetherian case), on the ring $Abowtie^fJ$. Among other things, we obtain a generalization of the well-known result that when the Nagatas idealization is Cohen-Macaulay.
Let $(A,mathfrak{m})$ be a Gorenstein local ring and let $CMS(A)$ be its stable category of maximal CM $A$-modules. Suppose $CMS(A) cong CMS(B)$ as triangulated categories. Then we show (1) If $A$ is a complete intersection of codimension $c$ then so is $B$. (2) If $A, B$ are Henselian and not hypersurfaces then $dim A = dim B$. (3) If $A, B$ are Henselian and $A$ is an isolated singularity then so is $B$. We also give some applications of our results.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
