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Near-rings associated with matched pairs on ring modules

Authors: C. J. Maxson and A. P. J. van der Walt
Journal: Proc. Amer. Math. Soc. 122 (1994), 665-675
MSC: Primary 16Y30
MathSciNet review: 1203989
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Abstract: Let G be a module over a ring R, let $ \mathcal{C} = \{ {C_i}\}, i \in I$, be a family of submodules of G, and let $ \mathcal{H} = \{ {H_i}\}, i \in I$, where $ {H_i}$ is a subgroup of $ \operatorname{Hom}_R({C_i},G)$ with certain properties. To each such pair $ (\mathcal{C},\mathcal{H})$, a near-ring $ M(\mathcal{C},\mathcal{H})$ is associated, which is a generalization of the near-ring of homogeneous functions determined by (G, R). The transfer of information from module properties of $ {G_R}$ reflected in $ (\mathcal{C},\mathcal{H})$ to structural properties of $ M(\mathcal{C},\mathcal{H})$ is investigated.

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