Modules whose $p$-submodules are direct summands


Abstract: In this article we deal with modules with the property that all $p$-submodules are direct summands. In contrast to $CLS$-modules, it is shown that the former property is closed under finite direct sums, but it is not inherited by direct summands. Hence we focus on when the direct summands of aforementioned modules enjoy the property. Moreover, we characterize the forenamed class of modules in terms of lifting homomorphisms.

Keywords: Extending module, $CLS$ modules, $\pi$-extending module

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