Relative coherent modules and semihereditary modules

Abstract

Given a positive integer n, a left R-module M is called n-coherent (resp. n-semihereditary) if every n-generated submodule of M is finitely presented (resp. projective). We investigate the properties of n-coherent modules and n-semihereditary modules. Various results are developed, many extending known results.

Keywords:

• n-coherent module
• n-semihereditary module
• n-M-flat module
• n-M-injective module
• precover
• preenvelope

2010 Mathematics Subject Classification:

• 16P70
• 16D40
• 16D50

Additional information

Funding

This research was supported by NSFC (11771202), NSF of Jiangsu Province of China (BK20160771) and Nanjing Institute of Technology of China (CKJA201707, JCYJ201842). The author wants to express his gratitude to the referee for the very helpful comments and suggestions.