On Cofinitely Lifting and Cofinitely Weak Lifting Modules

Abstract

We say that a module M is lifting if M is amply supplemented and every supplement submodule of M is a direct summand. The module M is called cofinitely lifting if it is amply cofinitely supplemented and every supplement of any cofinite submodule of M is a direct summand. In this article various properties of cofinitely lifting modules are given. In addition, a generalization of cofinitely lifting modules is investigated.

Key Words:

• Cofinitely lifting module
• Cofinitely weak lifting module
• Lifting module
• Local module
• Weak lifting module

Mathematics Subject Classification:

• Primary 16D80
• Secondary 16D70, 16D99

Notes

Communicated by K. M. Rangaswamy.