模的Schröder-Bernstein问题
The Schröder-Bernstein problem for Modules
摘要：
本文研究模的Schröder-Bernstein问题。我们得到了Schröder-Bernstein问题的一个正解的模不变的自同态下的一般包络下的一些温和的条件下，总是满足，例如，在内射，纯内射或余挠包络的情况下。在内射包络和纯内射包络的特殊情况下，我们能够进一步扩展它，我们表明，施罗德-伯恩斯坦问题有一个积极的解决方案，即使是模不变，只有下自同构的内射包络或纯内射包络。
英文摘要：
In this paper we study the Schröder-Bernstein problem for modules. We obtain a positive solution for the Schröder-Bernstein problem for modules invariant under endomorphisms of their general envelopes under some mild conditions that are always satisfied, for example, in the case of injective, pure-injective or cotorsion envelopes. In the particular cases of injective envelopes and pure-injective envelopes, we are able to extend it further and we show that the Schröder-Bernstein problem has a positive solution even for modules that are invariant only under automorphisms of their injective envelopes or pure-injective envelopes.
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