arXiv subjects

Tran Do Minh Chau

Publications and source records attributed to Tran Do Minh Chau.

4 recordsLinked to original sources

arXiv2026

The transfer of Artinian and Cohen-Macaulay properties under module-finite extensions

This paper deals with certain classes of modules under module-finite extensions. Let $φ: R\hookrightarrow S$ be a module-finite extension between commutative Noetherian local rings. We investigate the transfer of Artinian module structures and attached primes between $R$ and $S$. We clarify the behavior of local cohomology modules as well as certain structures of finitely generated $S$-modules under the restriction of scalars to $R$ via $φ$. We show that $R$ is a quotient of a Cohen-Macaulay local ring if and only if so is $S$. As an application, we characterize the structure of Nagata's idealization. Using Macaulayfication of algebraic varieties and idealization, we give an example to illustrate the results.

math.AC↗

arXiv2026

Cohen-Macaulayness of formal fibers and dimension of local cohomology modules

Let $(R, \mathfrak{m} )$ be a Noetherian local ring, $M$ a finitely generated $R$-module of dimension $d$. Set $\mathfrak{a}(M):=\mathfrak{a}_0(M)\cdots \mathfrak{a}_{d-1}(M)$, where $\mathfrak{a}_i(M):={\rm Ann}_RH^i_{\mathfrak{m}}(M)$ for $i\geq 0$. In this paper, we study the Cohen-Macaulayness of formal fibers of $R$ in the relation with the dimension ${\rm dim} (R/\mathfrak{a}(M)).$ We prove that ${\rm dim} (R/\mathfrak{a}(M)) {\rm dim} (R/\mathfrak{a}(M)).$ As applications, we explore the structure of local rings and the dimension, the closedness of non Cohen-Macaulay locus of finitely generated modules.

math.AC↗

arXiv2025

Ascent and descent of Artinian module structures under flat base changes

Let $φ: R\rightarrow S$ be a flat local homomorphism between commutative Noetherian local rings. In this paper, the ascent and descent of Artinian module structures between $R$ and $S$ are investigated. For an Artinian $R$-module $A$, the structure of $A\otimes_RS$ is described. As an application, the Artinianess of certain local cohomology modules is clarified.

math.AC↗

arXiv2017

Sally modules of canonical ideals in dimension one and 2-AGL rings

The notion of 2-AGL ring in dimension one which is a natural generalization of almost Gorenstein local ring is posed in terms of the rank of Sally modules of canonical ideals. The basic theory is developed, investigating also the case where the rings considered are numerical semigroup rings over fields. Examples are explored.

math.AC↗