∞-costar modules

Abstract

In this article, we study a natural generalization of finitistic n-self-cotilting modules (and hence also of costar-modules) by introducing the notion of ∞-costar modules over any ring R. The most important results about finitistic n-self-cotilting modules and costar modules are generalized. Also, we introduce a subclass of ∞-costar modules, which is a natural generalization of cotilting modules of finite injective dimensions to infinite injective dimensions. When R is a finite dimensional K-algebra, a finitely generated ∞-costar module is an ∞-cotilting module.

Keywords:

• Costar module
• cotilting module
• finitistic n-self-cotilting modules

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 13D02
• 16D90
• 16E30

Acknowledgment

The authors would like to express their sincere thanks to the referee for his or her careful reading of the manuscript and helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was partially supported by the ShanDong Provincial Natural Science Foundation of China (No. ZR2015PA001), a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, and the National Natural Science Foundation of China (No. 11771212).