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When are induction and coinduction functors isomorphic? (English) Zbl 0815.18006

It is well known that if \(R\) is a strongly graded ring, then the induced and coinduced functors associated to \(R\) are isomorphic. The paper investigates how close is a graded ring for which the two functors are isomorphic to being strongly graded. The problem of when the two functors are isomorphic is also studied in the nongraded case, as well as in the general case of Grothendieck categories.

MSC:

18E15 Grothendieck categories (MSC2010)
16B50 Category-theoretic methods and results in associative algebras (except as in 16D90)
16W50 Graded rings and modules (associative rings and algebras)
18A22 Special properties of functors (faithful, full, etc.)
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