Xiaolei Zhang

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20242026

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4 papers · 1 filter

math.RA2025

On the existence of parameterized noetherian rings

Xiaolei Zhang

A ring $R$ is called left strictly $(< ℵ_{α})$ -noetherian if $ℵ_{α}$ is the minimum cardinal such that every ideal of $R$ is $(< ℵ_{α})$ -generated. In this note, we show tha…

math.RA2025

Characterizing categoricity in the class $A dd (M)$

Xiaolei Zhang

We study categoricity of the additive closure $Add (M)$ , consisting of all direct summands of arbitrary direct sums of copies of a fixed module $M$ . For an $η$ -genera…

math.RA2024

The Schröder-Bernstein problem for relative injective modules

Xiaolei Zhang

Let $(K, M)$ be a pair satisfying some mild condition, where $K$ is a class of $R$ -modules and $M$ is a class of $R$ -homomorphisms. We show that if $f : A \to B$ and $g:B\right…

math.RA2024

Some remarks on injective envelopes on ring extensions

Xiaolei Zhang

Let $f : S \to R$ be a ring extension. We introduce and study the properties of $(R, S)_{⋆}$ -injective modules and the existences of $(R, S)_{⋆}$ -injective envelopes. Besi…

On the existence of parameterized noetherian rings

Characterizing categoricity in the class Add(M)

The Schröder-Bernstein problem for relative injective modules

Some remarks on injective envelopes on ring extensions

Characterizing categoricity in the class $A dd (M)$