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Gradings of finite support. Application to injective objects. (English) Zbl 0859.16036
The relationship between injectivity in \(R\)-gr and \(R\)-mod is studied, where \(R\) is a group-graded ring. The second author proved that if \(R\) has finite support, then gr-injective modules with finite support are injective in \(R\)-mod. This result is generalized by showing that the condition that \(R\) have finite support is not necessary. It is also shown that the theory of graded rings and modules with finite support does not coincide with the theory of finite group gradings.

MSC:
16W50 Graded rings and modules (associative rings and algebras)
16D50 Injective modules, self-injective associative rings
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