# The π-extending Property via Singular Quotient Submodules

• Kara, Yeliz (Department of Mathematics, Bursa Uludag University) ;
• Tercan, Adnan (Department of Mathematics, Hacettepe University)
• Accepted : 2018.08.13
• Published : 2019.09.23
• 14 2

#### 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.

#### Keywords

extending modules;${\pi}$-extending module;projection invariant

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