Kyungpook Mathematical Journal

  • 제59권3호
  • /
  • Pages.391-401
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  • 2019
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  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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The π-extending Property via Singular Quotient Submodules

  • Kara, Yeliz (Department of Mathematics, Bursa Uludag University) ;
  • Tercan, Adnan (Department of Mathematics, Hacettepe University)
  • 투고 : 2018.03.27
  • 심사 : 2018.08.13
  • 발행 : 2019.09.23
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초록

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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참고문헌

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