On projectivity of finitely generated modules

Abstract

In a recent paper of Holston, López-Permouth, Mastromatteo and Simental-Rodriguez, a ring R is defined to have no subprojective middle class if the subprojectivity domain of any R-module is the smallest or largest possible. In this work, we continue to use this idea of restricting the class of subprojectivity domains to classify rings. A finitely generated (resp., cyclic) module is called fingp-indigent (resp., singp-indigent), if its subprojectivity domain consists of only finitely projective (resp., singly projective) modules. We give a characterization of rings over which finitely generated (resp., cyclic) modules are either projective or fingp-indigent (resp., singp-indigent).

Keywords:

• Fingp-indigent
• finitely (singly) projective module
• singp-indigent
• subprojectivity domain

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16D10
• 16D40

Acknowledgments

The authors are deeply grateful to the referee for his/her careful reading of the paper and valuable suggestions.

Disclosure Statement

The authors report there are no competing interests to declare.

Funding

Türkiye Bilimsel ve Teknolojik Araştırma Kurumu;

Additional information

Funding

This work was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under Grant number 122F130.