On a class of Golod homomorphisms.
On a functional equation arising from hyperbolic geometry.
On a Geometric Interpretation of Multiplicity.
On a result of avramov.
On a theorem of F. S. Macaulay on colon ideals.
On Almost Complete Intersections.
On Castelnuovo's regularity and Hilbert functions
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 Cohen-Macaulay rings
In this paper, we use a characterization of -modules such that to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting to be the local cohomology functor of with respect to the maximal ideal where is the Krull dimension of .
On commutative rings whose prime ideals are direct sums of cyclics
In this paper we study commutative rings whose prime ideals are direct sums of cyclic modules. In the case is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it is shown that for a local ring , the following statements are equivalent: (1) Every prime ideal of is a direct sum of cyclic -modules; (2) where is an index set and is a principal ideal ring for each ; (3) Every prime ideal of is a direct sum of at most...
On equimultiple ideals.
On equimultiple subschemes of a local scheme over a field of characteristic zero
On h-regular graded algebras
On h-regular grades algebras of characteristic p > 0
On -sequences associated to filtrations
On mixed multiplicities of homogeneous ideals.
On Monomial curves and Cohen-Macaulay type.
On Monomial k-Buchsbaum curves in P3.
On multipliciteis of local rings.
On multi-Rees algebras. With an Appenddix by Ngô Viêt Trung.