Static modules and equivalences
نویسنده
چکیده
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.
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