6 papers
On embeddings of rings into their canonical modules
Tran Nguyen An, Shinya Kumashiro, Mouma Samanta
We study embeddings of Cohen--Macaulay local rings into their canonical modules such that the quotient of the cokernel by a regular sequence has the residue field as a direct summa…
Irreducible multiplicity of idealizations
Tran Nguyen An
Let be a Noetherian local ring and a finitely generated -module. We study the relations of the index of reducibility and the irreducible multiplicity of a…
On depth of modules in an ideal
Tran Nguyen An
Let be a commutative Noetherian ring, an ideal of and a finitely generated -module with . Denote by $\depth_R(I,M)$ the depth of in . In \cit…
The irreducible multiplicity and Ulrich modules
Tran Nguyen An, Shinya Kumashiro
In this paper, we give a relation between the Hilbert multiplicity and the irreducible multiplicity. As an application, we characterize Ulrich modules in term of the irreducible mu…
Reducibility index and sum-reducibility index
Tran Nguyen An, Tran Duc Dung, Shinya Kumashiro +1
Let be a Noetherian ring. For a finitely generated -module , Northcott introduced the reducibility index of , which is the number of submodules appearing in an irredun…
Sequentially Cohen-Macaulay Rees algebras
Naoki Taniguchi, Tran Thi Phuong, Nguyen Thi Dung +1
This paper studies the question of when the Rees algebras associated to arbitrary filtration of ideals are sequentially Cohen-Macaulay. Although this problem has been already inves…