Longueurs de modules constructibles et valuations
Maximal non-Jaffard subrings of a field.
A domain R is called a maximal non-Jaffard subring of a field L if R ⊂ L, R is not a Jaffard domain and each domain T such that R ⊂ T ⊆ L is Jaffard. We show that maximal non-Jaffard subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dimv R = dim R + 1. Further characterizations are given. Maximal non-universally catenarian subrings of their quotient fields are also studied. It is proved that this class of domains coincides with the previous class when R is integrally...
Minimal injective resolutions
Minimal injective resolutions with applications to dualizing modules and Gorenstein modules
Modules of finite virtual projective dimension.
Modules with sliding depth.
Multiplicities and Hilbert Functions under Blowing Up.
Nagata rings and directed unions of Artinian subrings.
Notes on an extension of Krull's principal ideal theorem
On Almost Complete Intersections.
On Bhargava rings
Let be an integral domain with the quotient field , an indeterminate over and an element of . The Bhargava ring over at is defined to be . In fact, is a subring of the ring of integer-valued polynomials over . In this paper, we aim to investigate the behavior of under localization. In particular, we prove that behaves well under localization at prime ideals of , when is a locally finite intersection of localizations. We also attempt a classification of integral domains ...
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.