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Modules with the Closed Sum Property

机译:具有封闭总和属性的模块

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A module M is said to have the closed intersection property (briefly CIP) if, the intersection ofany two closed submodules of M is again closed [6]. In this paper we present the dual of theCIP, namely, M has the closed sum property (briefly CSP) for which the sum of any two closedsubmodules, so the submodule generated by their union, is a closed submodule, too. Weinvestigate the concept of CSP. Basic properties and some relations of these modules aregiven
机译:如果模块M的任何两个封闭子模块的交集再次被封闭,则称模块M具有封闭的交集属性(简称CIP)[6]。在本文中,我们介绍了CIP的对偶,即M具有封闭和属性(简称CSP),对于该属性,任何两个封闭子模块的和,因此,由它们的并集生成的子模块也是封闭子模块。我们研究了CSP的概念。给出了这些模块的基本属性和一些关系

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