Xiaolei Zhang

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20232026

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math.AC2026

The finitistic weak dimensions of Gaussian rings

Xiaolei Zhang

We prove that every commutative Gaussian ring has finitistic weak dimension at most two. The proof works with a fixed module of finite flat dimension and does not assume that the w…

math.AC2025

Module-Theoretic Characterizations of Prufer $v$ -Multiplication Domains

Xiaolei Zhang, Hwankoo Kim

We present unified $w$ -theoretic characterizations of Prüfer $v$ -multiplication domains (P $v$ MDs). A module-theoretic perspective shows that torsion submodules are $w$ -pure, and fo…

math.AC2023

On generalized fraction and power series properties of $S$ -Noetherian rings

Xiaolei Zhang

In this note, we study the generalized fraction properties and power series properties of $S$ -Noetherian rings. Actually, we investigate two questions proposed in [A. Dab…

math.AC2023

A note on a Cohen-type theorem for $w$ -Artinian modules

Xiaolei Zhang

In this note, we prove that a $w$ -module $M$ is $w$ -Artinian if and only if it is $w$ -cofinitely generated and for every prime $w$ -ideal $p$ of $R$ with $(0:_RM)\subsete…

The finitistic weak dimensions of Gaussian rings

Module-Theoretic Characterizations of Prufer v-Multiplication Domains

On generalized fraction and power series properties of S-Noetherian rings

A note on a Cohen-type theorem for w-Artinian modules

Module-Theoretic Characterizations of Prufer $v$ -Multiplication Domains

On generalized fraction and power series properties of $S$ -Noetherian rings

A note on a Cohen-type theorem for $w$ -Artinian modules