On Almost Complete Intersections.
On co-Gorenstein modules, minimal flat resolutions and dual Bass numbers
The dual of a Gorenstein module is called a co-Gorenstein module, defined by Lingguang Li. In this paper, we prove that if R is a local U-ring and M is an Artinian R-module, then M is a co-Gorenstein R-module if and only if the complex is a minimal flat resolution for M when we choose a suitable triangular subset on R̂. Moreover we characterize the co-Gorenstein modules over a local U-ring and Cohen-Macaulay local U-ring.
On Projective Modules.
On some results of L. J. Ratliff
On Symmetric Algebras which are Cohen Macaulay.
On the Deviation and the Type of a Cohen-Macaulay Ring.
On the Forster-Eisenbud-Evans Conjectures.
On the Grade of Some Ideals.
On the grades of order ideals.
On the Length of Faithful Modules over Artinian Local Rings.
On the Regularity of Graded k-Algebras of Krull Dimension ...1.
On the symmetric algebra of certain first syzygy modules
Let be a standard graded -algebra over a field . Then can be written as , where is a graded ideal of a polynomial ring . Assume that and is a strongly stable monomial ideal. We study the symmetric algebra of the first syzygy module of . When the minimal generators of are all of degree 2, the dimension of is calculated and a lower bound for its depth is obtained. Under suitable conditions, this lower bound is reached.
On the upper semicontinuity intersection defect.
On Two Conjectures About Polynomial Rings.