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Maximal elements of support. (English) Zbl 0984.13001
Let \(R\) be a commutative ring with 1. In this paper the author claims that the Jacobson radical of an \(R\)-module \(M\) is tightly related to the support of \(M\), where the support of \(M\) is the set of prime ideals \(P\) such that the localization of \(M\) at \(P\) is not zero. In particular, if the module is finitely generated and injective, the set of zero divisors of the module is equal to the union of the maximal elements of the support of the module.
Reviewer: K.Koh (Raleigh)
MSC:
13A10 Radical theory on commutative rings (MSC2000)
13C11 Injective and flat modules and ideals in commutative rings
13E15 Commutative rings and modules of finite generation or presentation; number of generators
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