Graded Weakly 2-Absorbing Ideals over Non-Commutative Graded Rings

Normal Ideals of Graded Rings

For a graded domain R = k[X0, ...,Xm]/J over an arbitrary domain k, it is shown that the ideal generated by elements of degree ≥ mA, where A is the least common multiple of the weights of the Xi, is a normal ideal.

Some Properties of Non-commutative Regular Graded Rings

Introduction. Let A be a noetherian ring. When A is commutative (of finite Krull dimension), A is said to be Gorenstein if its injective dimension is finite. If A has finite global dimension, one says that A is regular. If A is arbitrary, these hypotheses are not sufficient to obtain similar results to those of the commutative case. To remedy this problem, M. Auslander has introduced a suppleme...

Graded Rings Associated with Contracted Ideals

The study of the ideals in a regular local ring (R,m) of dimension 2 has a long and important tradition dating back to the fundamental work of Zariski [ZS]. More recent contributions are due to several authors including Cutkosky, Huneke, Lipman, Sally and Tessier among others, see [C1, C2, H, HS, L, LT]. One of the main result in this setting is the unique factorization theorem for complete (i....

On Associated Graded Rings of Normal Ideals

On 2-absorbing Primary Submodules of Modules over Commutative Rings

All rings are commutative with 1 6= 0, and all modules are unital. The purpose of this paper is to investigate the concept of 2-absorbing primary submodules generalizing 2-absorbing primary ideals of rings. Let M be an R-module. A proper submodule N of an R-module M is called a 2-absorbing primary submodule of M if whenever a, b ∈ R and m ∈M and abm ∈ N , then am ∈M -rad(N) or bm ∈M -rad(N) or ...