PDF(431 KB)
PDF(431 KB)
PDF(431 KB)
Gorenstein范畴上的一个问题
On a Question of Gorenstein Categories
设A是阿贝尔范畴，X是A的子范畴.Sather-Wagstaff，Sharif和White引入了Gorenstein子范畴的概念，记为G（X）.我们用PP（相应地，P）代表纯投射R-模类（相应地，投射R-模类）.本文给出了一类满足条件“G（P）⊆G（PP）”的环，由此给出了当W是X的子范畴时，G（W）是否包含在G（X）中的一个否定回答.进一步，刻画了包含关系G（P）⊆G（PP）和G（PP）⊆G（P）何时成立.
Let A be an abelian category and X a subcategory of A. Sather-Wagstaff, Sharif and White introduced the Gorenstein subcategory G (X). Denote by PP the class of pure-projective R-modules and by P the class of projective R-modules. We show that there are some rings such that G (P) ⊆ G(PP), which gives a negative answer to the Question that whether G (W) is contained in G (X) provided that W is a subcategory of X. In addition, we give some characterizations of when G (P) ⊆ G (PP) and G (PP) ⊆ G (P) hold.
纯投射模 / Gorenstein投射模 / Gorenstein范畴 {{custom_keyword}} /
pure-projective module / Gorenstein projective module / Gorenstein category {{custom_keyword}} /
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国家自然科学基金（11501257，11671069，11771212）；中国博士后科学基金（2016M600426）；浙江省自然科学基金（LY18A010032）；中国留学基金委资助项目；江苏高校“青蓝工程”资助项目
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