Subinjective portfolios and rings with a linearly ordered subinjective profile


Alizade R., Diril M., DURĞUN Y.

Communications in Algebra, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2024
  • Doi Number: 10.1080/00927872.2024.2377807
  • Journal Name: Communications in Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: subinjective portfolio, Subinjective profile, Subinjectivity domain
  • Çukurova University Affiliated: Yes

Abstract

In this paper we study subinjectivity domains of various R-modules and inclusion relations between these domains. We show that if the class of all subinjectivity domains is linearly ordered, then R is right Noetherian, and is either a right V-ring or a ring with unique noninjective simple module U. For the latter case, if U is projective but not indigent, then there exists a ring decomposition (Formula presented.) such that S is a semisimple Artinian ring and T is an indecomposable right Artinian right hereditary ring. Also, in that case, if the subinjectivity domain of U is the only middle subinjectivity domain, then R is right Artinian.