On the module of homomorphisms on finitely generated multiplication modules II.
Copyright policy )On the module of homomorphisms on finitely generated multiplication modules II.
[For part I see ibid. 22, No. 2, 97-105 (1991; see the preceding review).] Let \(R\) be a commutative ring with 1. Let \(A\) be a finitely generated multiplication unitary (left) \(R\)-module, \(B\) a multiplication \(R\)- module, and let \(E=E(A,B)=[\text{ann} B:\text{ann} A]\). It turns out that \(EB=\sum_{f\in\text{Hom}(A,B)}f(A)\). --- We show that some of the properties of \(\text{Hom}(A,B)\) are determined by those of \(EB\) and conversely.
Commutative rings and modules of finite generation or presentation; number of generators, module of homomorphisms, multiplication module, multiplication modules, Divisibility and factorizations in commutative rings, Morphisms of commutative rings
Commutative rings and modules of finite generation or presentation; number of generators, module of homomorphisms, multiplication module, multiplication modules, Divisibility and factorizations in commutative rings, Morphisms of commutative rings
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