On Direct Projective H-Supplemented Modules

Abstract

In this paper, we consider a direct projective H-supplemented module which is a generalization of a discrete module (cf. [11, 16]). We prove that any direct projective H-supplemented module satisfies the exchange property and also shows that if M₁ and M₂ are direct projective H-supplemented modules, then M = M₁ ⊕ M₂ is direct projective H-supplemented if and only if M_i is radical M_j-projective (i ≠ j).

Key Words:

• Direct projective module
• Discrete module
• H-supplemented module
• (Internal) exchange property
• Radical projective

2000 Mathematics Subject Classification:

• Primary: 16D40
• Secondary: 16D70

ACKNOWLEDGMENTS

The authors would like to thank Professor Hiroshi Yoshimura for valuable comments. The authors are also grateful to the referee for the suggestions which improved the presentations of the paper. This work was supported by JSPS KAKENHI Grant Number 15K04821.