Summand intersection property of modules via z-closed submodules

Mutlu F. T., TERCAN A.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.15, no.07, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 07
  • Publication Date: 2022
  • Doi Number: 10.1142/s1793557122501248
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: SIP, z-closed submodule, extending module, RINGS
  • Hacettepe University Affiliated: Yes


In this paper, we define a module M . to be SIPz if and only if intersection of each pair of z-closed direct summands is also a direct summand of M. We investigate structural properties of SIPz-modules and locate the implications between the other module properties which are essentially based on direct summands. We deal with decomposition theory as well as direct summands of SIPz -modules. We apply our results to matrix rings. To this end, it is obtained that the SIPz property is not Morita invariant..