Static modules and equivalences
Static modules and equivalences
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DOI：
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发表时间：
2000
影响因子：
1.4
通讯作者：
K. Fuller;A. Kashu;T. Kato;C. Menini;T. Onodera
中科院分区：
文献类型：
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作者：
K. Fuller;A. Kashu;T. Kato;C. Menini;T. Onodera
根据K. Morita，环R和S上的满模范畴之间的任何等价性都由双模RPS给出，使得RP是R-Mod中的一个R-生成的投射生成元，S = EndR（P）.有各种各样的论文以类似的方式描述了R-Mod和S-Mod的某些子类别之间的等价性，并具有RPS的适当性质。这里我们从另一面开始：给定任何双模RPS，我们要求函子HomR（P，-）相互等价的子范畴。在R-Mod中，这些是P -静态（= P -可解）模。在此背景下，s-ε-拟投射，w-ε-拟投射和（自）倾斜模RP的性质被重新考虑，以及PS的Mittag-Leffler性质。此外，对任意环扩张R→ A，研究了A-模A <$RP的相关性质。
By a well known theorem of K. Morita, any equivalence between full module categories over rings R and S, are given by a bimodule RPS , such that RP is a finitely generated projective generator in R-Mod and S = EndR(P ). There are various papers which describe equivalences between certain subcategories of R-Mod and S-Mod in a similar way with suitable properties of RPS . Here we start from the other side: Given any bimodule RPS we ask for the subcategories which are equivalent to each other by the functor HomR(P,−). In R-Mod these are the P -static (= P -solvable) modules. In this context properties of s-Σ-quasi-projective, w-Σ-quasi-projective and (self-) tilting modules RP are reconsidered as well as Mittag-Leffler properties of PS . Moreover for any ring extension R→ A related properties of the A-module A⊗R P are investigated.