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PDF(402 KB)
PDF(402 KB)
复形的#-内射包络的存在性
The Existence of #-injective Envelopes of Complexes
令dwI表示所有#-内射左R-模复形构成的类（即内射左R-模的复形构成的类）.本文证明了在左诺特环R上（⊥（dwI），dwI）是完备的内射余挠对.特别地，我们得到每个左R-模复形都有#-内射包络.作为应用，证明了在左诺特环R上，每个左R-模复形都有特殊Etac（I）-预包络，其中Etac（I）是所有内射左R-模的完全零调复形构成的类.
Let dwI denote the class of #-injective complexes of left R-modules (i.e., complexes of injective left R-modules). We prove that over left noetherian rings R, the pair (⊥(dwI), dwI) is a perfect injective cotorsion pair. In particular, we get that every complex of left R-modules has a #-injective envelope. As an application, we prove that over left noetherian rings R, every complex of left R-modules has a special Etac (I)-preenvelope, where Etac (I) is the class of complete acyclic complexes of injective left R-modules.
#-内射复形 / 覆盖 / 包络 / 余挠对 {{custom_keyword}} /
#-injective complex / cover / envelope / cotorsion pair {{custom_keyword}} /
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国家自然科学基金资助项目（11761045，11561039）；甘肃省自然科学基金资助项目（18JR3RA113，17JR5RA091）；兰州交通大学"百名青年优秀人才培养计划"基金资助项目
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