AI 中文总结
本文研究强G-正则环，证明其与拟支配环及厚子范畴的共变/反变有限性密切相关，并否定回答Chen的问题，指出Auslander-Ringel-Tachikawa定理的Gorenstein投射类似结论对弱Gorenstein交换局部阿廷代数不成立。
AI 中文摘要
诺特环被称为G-正则环，当所有有限生成的Gorenstein投射模都是投射模时。本文研究满足更强条件的环，即所有Gorenstein投射模都是投射模，我们将这类环称为强G-正则环。我们证明强G-正则环的概念与Takahashi引入的拟支配环概念、以及某一厚子范畴的共变/反变有限性密切相关。我们还否定地回答了Chen提出的一系列问题，表明即使对于Ringel和Zhang意义下弱Gorenstein的交换局部阿廷代数，Auslander-Ringel-Tachikawa定理的Gorenstein投射类似结论也不成立。
英文摘要
A noetherian ring is called G-regular when all finitely generated Gorenstein projective modules are projective. In this paper, we study rings satisfying the stronger condition that all Gorenstein projective modules are projective, which we call strongly G-regular. We show that the notion of strongly G-regular rings is closely related to that of quasi-dominant rings introduced by Takahashi and to the covariant/contravariant finiteness of a certain thick subcategory. We also answer a series of questions due to Chen in the negative, showing that the Gorenstein projective analogue of the Auslander-Ringel-Tachikawa theorem fails even for commutative local artin algebras which are weakly Gorenstein in the sense of Ringel and Zhang.
Comments19 pages
