Extending properties of exact projection invariant submodules


Tercan A., Yucel C. C.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.15, no.08, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 08
  • Publication Date: 2022
  • Doi Number: 10.1142/s1793557122501480
  • Journal Name: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index, Scopus, zbMATH
  • Keywords: Projection invariant submodule, ep-submodule, left exact preradical, ES-module, Goldie extending module, MODULES

Abstract

In this paper, on using a left exact preradical, we define a module M to be EPD (EPG) if and only if each ep-submodule X of M is a direct summand (there exists a direct summand D such that X boolean AND D is essential in both X and D). We investigate structural properties of former new classes of modules and locate the implications between the other extending properties. We deal with decomposition theory as well as ring and module extensions for EPD and EPG-modules. We show that the EPD property is inherited by finite direct sums however we provide algebraic topological examples which show that direct summands do not enjoy the property. Moreover, we obtain that EPG property is closed under right essential overring and rational hull. We provide examples to illustrate some of the results by making special choices of left exact preradicals.