Publication:
The π-extending property via singular quotient submodules

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Date

2019-09-01

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Kyungpook Natl Univ, Dept Mathematics

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Abstract

A module is said to be pi-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this article, we focus on the class of modules having the pi-extending property by looking at the singularity of quotient submodules. By doing so, we provide counterexamples, using hypersurfaces in projective spaces over complex numbers, to show that being generalized pi-extending is not inherited by direct summands. Moreover, it is shown that the direct sums of generalized pi-extending modules are generalized pi-extending.

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Modules, Extending modules, Pi-extending module, Projection invariant, Science & technology, Physical sciences, Mathematics

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