Bounding the degrees of generators of a homogeneous dimension 2 toric ideal.
Bounding the Number of Generators of a Module.
Bounds and definablity over fields.
Bounds for the multiplicity of almost complete intersections.
Bounds on Bass numbers and their dual
Let be a commutative Noetherian local ring. We establish some bounds for the sequence of Bass numbers and their dual for a finitely generated -module.
Calcul différentiel extérieur de dégré arbitraire.
Calculs sur les modules projectifs
Cancellative relations and matrices
Castelnuovo-Mumford regularity of products of ideals.
The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask,...
Cellular covers of cotorsion-free modules
In this paper we improve recent results dealing with cellular covers of R-modules. Cellular covers (sometimes called colocalizations) come up in the context of homotopical localization of topological spaces. They are related to idempotent cotriples, idempotent comonads or coreflectors in category theory. Recall that a homomorphism of R-modules π: G → H is called a cellular cover over H if π induces an isomorphism , where π⁎(φ) = πφ for each (where maps are acting on the left). On the one hand,...
CF-modules over commutative rings
Let be a commutative ring with unit. We give some criterions for determining when a direct sum of two CF-modules over is a CF-module. When is local, we characterize the CF-modules over whose tensor product is a CF-module.
Chains of free modules and construction of -free modules
Characterization of the Hilbert-Samuel polynomials of curve singularities
Characterizations of incidence modules
Let be an associative ring and be a left -module. We introduce the concept of the incidence module of a locally finite partially ordered set over . We study the properties of and give the necessary and sufficient conditions for the incidence module to be an IN-module, -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of -modules is closed under direct product and upper triangular matrix modules.
Characterizations of some rings with -projective, -(FP)-injective and -flat modules
Let be a commutative ring and a semidualizing -module. We investigate the relations between -flat modules and -FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.
Chern classes of matrices over Noetherian rings.
Cohen-Macaulay and Gorenstein property of rees algebras of non-singular equimultiple prime ideals.
Cohen-Macaulay Rees algebras and degrees of polynomial relations.
Cohen-Macaulayness of multiplication rings and modules
Let R be a commutative multiplication ring and let N be a non-zero finitely generated multiplication R-module. We characterize certain prime submodules of N. Also, we show that N is Cohen-Macaulay whenever R is Noetherian.
Cohen-Macauly Graphs.