Subinjective portfolios and rings with a linearly ordered subinjective profile

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 $R=S\times T$ 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.

KEYWORDS:

• Subinjective profile
• subinjective portfolio
• Subinjectivity domain

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16D10
• 16D50

Acknowledgments

The second author expresses her sincere thanks to TÜBİTAK-BİDEP for her PhD scholarship award. All authors would like to thank the referee for the valuable comments and suggestions in shaping the article into its present form.

Disclosure statement

The authors declare that they have no conflicts of interest.

Additional information

Funding

This work was supported by the Scientific and Technological Research Council of Türkiye (TUBITAK)(Project number: 122F130).