SUMMAND INTERSECTION PROPERTY ON THE CLASS OF EXACT SUBMODULES

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Mutlu F. T., TERCAN A.

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, cilt.111, sa.125, ss.61-68, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 111 Sayı: 125
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2298/pim2225061t
  • Dergi Adı: PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
  • Sayfa Sayıları: ss.61-68
  • Anahtar Kelimeler: SIP, SIPr, preradical, exact submodule, direct summand, MODULES
  • Hacettepe Üniversitesi Adresli: Evet

Özet

A module M is said to have the SIP if intersection of each pair of direct summands is also a direct summand of M. In this article, we define a module M to have the SIPr if and only if intersection of each pair of exact direct summands is also a direct summand of M where r is a left exact preradical for the category of right modules. We investigate structural properties of SIPr-modules and locate the implications between the other summand intersection properties. We deal with decomposition theory as well as direct summands of SIPr-modules. We provide examples by looking at special left exact preradicals.