相对注入模块的施罗德-伯恩斯坦问题

arXiv - MATH - Rings and Algebras Pub Date : 2024-09-06 DOI:arxiv-2409.03972

Xiaolei Zhang

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引用次数: 0

摘要

让$(K,\M)$是一对满足某种温和条件的对，其中$K$是一类$R$模块，而$\M$是一类$R$同态。我们证明，如果$f:A/arightrow B$和$g:B/arightrow A$是$M$-嵌入，并且$A,B$是$K_\M$-注入，那么$A$与$B$同构，正面回答了Marcos和Jiri提出的问题[6]。

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The Schröder-Bernstein problem for relative injective modules

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 $f:A\rightarrow B$ and $g:B\rightarrow A$ are $\M$-embeddings and $A,B$ are $K_\M$-injective, then $A$ is isomorphic to $B$, positively answering an question proposed by Marcos and Jiri [6].

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arXiv - MATH - Rings and Algebras

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