Let be a commutative Noetherian ring and let I be a proper ideal of . D’Anna and Fontana in [6] introduced a new construction of ring,  named amalgamated duplication of along I. In this paper by considering the ring homomorphism , it is shown that if , then , also it is proved that if , then there exists  such that . Using this result it is shown that if is generically Cohen-Macaulay (resp. gen...

Let X ⊂ P be a generically reduced projective scheme. A fundamental goal in computational algebraic geometry is to compute information about X even when defining equations for X are not known. We use numerical algebraic geometry to develop a test for deciding if X is arithmetically Gorenstein and apply it to three secant varieties.

Given a commutative noetherian non-positive DG-ring with bounded cohomology which has dualizing DG-module, we study its regular, Gorenstein and Cohen-Macaulay loci. We give sufficient condition for the regular locus to be open, show that is always open. However, both of these loci are often empty: no matter how nice H0(A) is, there examples where A empty. then DG-module contains dense open set....

A Gorenstein sequence H is a sequence of nonnegative integers H = (1, h1, . . . , hj = 1) symmetric about j/2 that occurs as the Hilbert function in degrees less or equal j of a standard graded Artinian Gorenstein algebra A = R/I , where R is a polynomial ring in r variables and I is a graded ideal. The scheme PGor(H) parametrizes all such Gorenstein algebra quotients of R having Hilbert functi...

We develop in this paper a stable theory for projective complexes, by which we mean to consider chain complex of finitely generated modules as an object the factor category homotopy modulo split complexes. As result are able prove that over generically Gorenstein ring is exact if and only its dual exact. This shows dependence total reflexivity conditions ring.

A central problem in liaison theory is to decide whether every arithmetically Cohen-Macaulay subscheme of projective n-space can be linked by a finite number of arithmetically Gorenstein schemes to a complete intersection. We show that this can be indeed achieved if the given scheme is also generically Gorenstein and we allow the links to take place in an (n + 1)-dimensional projective space. F...

In an earlier work, we gave (additive) categorification of Grassmannian cluster algebras using the category CM(A) Cohen-Macaulay modules for a certain Gorenstein order A. this paper, each tilting object in CM(A), construct compatible pair (B,L) way that is consistent with mutation. This then determines quantum algebra and show that, when comes from rank one summands, (generically) isomorphic to...

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

Let R be a ring and n a fixed positive integer, we investigate the properties of n-strongly Gorenstein projective, injective and flat modules. Using the homological theory , we prove that the tensor product of an n-strongly Gorenstein projective (flat) right R -module and projective (flat) left R-module is also n-strongly Gorenstein projective (flat). Let R be a coherent ring ,we prove that the...