-anneaux noethériens
-depth on -modules and local cohomology
Let be a Noetherian ring, and and be two ideals of . Let be a Serre subcategory of the category of -modules satisfying the condition and be a -module. As a generalization of the - and , the - of on is defined as --, and some properties of this concept are investigated. The relations between - and are studied, and it is proved that -, where is a Serre subcategory closed under taking injective hulls. Some conditions are provided that local cohomology modules with...
-pure submodules.
Sagbi bases with applications to blow-up algebras.
S-divisible modules over domains.
Secondary characteristic classes and intermediate Jacobians.
Semicontinuity for representations of one-dimensional Cohen-Macaulay rings.
Semisimple Algebras and a Cancellation Law.
Separable -free modules with almost trivial dual
An -module has an almost trivial dual if there are no epimorphisms from to the free -module of countable infinite rank . For every natural number , we construct arbitrarily large separable -free -modules with almost trivial dual by means of Shelah’s Easy Black Box, which is a combinatorial principle provable in ZFC.
Sequences between d-sequences and sequences of linear type
The notion of a d-sequence in Commutative Algebra was introduced by Craig Huneke, while the notion of a sequence of linear type was introduced by Douglas Costa. Both types of sequences generate ideals of linear type. In this paper we study another type of sequences, that we call c-sequences. They also generate ideals of linear type. We show that c-sequences are in between d-sequences and sequences of linear type and that the initial subsequences of c-sequences are c-sequences. Finally we prove a...
Simple Flat Extensions. II.
Simple injective modules.
Small almost free modules with prescribed topological endomorphism rings
Some morphisms of modules over the ring of pseudorational numbers.
Some new results on numbers of generators of ideals in local rings
Some properties of Butler modules over valuation domains
Some properties of direct sums of uniserial modules over valuation domains
Some properties of the ideal of continuous functions with pseudocompact support.
Some properties of the zero divisor graph of a commutative ring
Let Γ(R) be the zero divisor graph for a commutative ring with identity. The k-domination number and the 2-packing number of Γ(R), where R is an Artinian ring, are computed. k-dominating sets and 2-packing sets for the zero divisor graph of the ring of Gaussian integers modulo n, Γ(ℤₙ[i]), are constructed. The center, the median, the core, as well as the automorphism group of Γ(ℤₙ[i]) are determined. Perfect zero divisor graphs Γ(R) are investigated.
Some remarks on generalized Cohen-Macaulay rings.