Tran Nguyen An

collaborators

3 papers

math.AC2025

Irreducible multiplicity of idealizations

Tran Nguyen An

Let $(R, m)$ be a Noetherian local ring and $M$ a finitely generated $R$ -module. We study the relations of the index of reducibility and the irreducible multiplicity of a…

math.AC2025

On depth of modules in an ideal

Tran Nguyen An

Let $R$ be a commutative Noetherian ring, $I$ an ideal of $R$ and $M$ a finitely generated $R$ -module with $dim_{R} (M) = d$ . Denote by $\depth_R(I,M)$ the depth of $M$ in $I$ . In \cit…

math.AC2025

The Depth Formula for modules over quotients of Gorenstein rings

Tran Nguyen An, Pham Hung Quy

A foundational result by C. Huneke and V. Trivedi provides a formula for the depth of an ideal in terms of height, computed over a finite set of prime ideals, for rings that are ho…