Some Aspects of Strongly P-projective Modules and Homological Dimensions

Abstract

A left R-module M is called strongly P-projective if Extⁱ(M, P) = 0 for all projective left R-modules P and all i ≥ 1. In this article, we first discuss properties of strongly P-projective modules. Then we introduce and study the strongly P-projective dimensions of modules and rings. The relations between the strongly P-projective dimension and other homological dimensions are also investigated.

Key Words:

• Gorenstein projective modules
• Precover
• Preenvelope
• Strongly P-projective module
• Strongly P-projective dimension
• Weakly Gorenstein flat module

2010 Mathematics Subject Classification:

• 16D40
• 16D50
• 18G20

ACKNOWLEDGMENTS

This research was supported by NSFC (11071111, 11171149), NSF of Jiangsu Province of China (BK2011068), Jiangsu 333 Project, Jiangsu Qinglan Project, Jiangsu Six Major Talents Peak Project. The author would like to thank the referee for his/her nice comments about this article.

Notes

Communicated by Q. Wu.