In this paper, we thoroughly study the Nakayama property and some related concepts. Also, we describe multiplication modules that, among other things, satisfy the Nakayama property. Next, we show that a ring 𝑅 is a Max ring if and only if all modules that can be generated by a finite or countable set have the weak Nakayama property. We prove that a ring 𝑅 is a perfect ring if and only if every module that can be generated by a finite or countable set has the Nakayama property. Finally, we present some categorical results on the aforementioned properties.

中文翻译：

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关于模块的 Nakayama 属性


在本文中，我们深入研究了中山性质和一些相关概念。此外，我们还描述了满足中山性质的乘法模块。接下来，我们证明环 𝑅 是 Max 环当且仅当所有可由有限或可数集生成的模都具有弱 Nakayama 性质。我们证明环 𝑅 是完美环当且仅当可由有限或可数集生成的每个模都具有 Nakayama 性质。最后，我们提出了上述属性的一些分类结果。