SUMMAND INTERSECTION PROPERTY ON THE CLASS OF EXACT SUBMODULES


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Mutlu F. T. , TERCAN A.

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, vol.111, no.125, pp.61-68, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 111 Issue: 125
  • Publication Date: 2022
  • Doi Number: 10.2298/pim2225061t
  • Journal Name: PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
  • Page Numbers: pp.61-68
  • Keywords: SIP, SIPr, preradical, exact submodule, direct summand, MODULES
  • Hacettepe University Affiliated: Yes

Abstract

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.