Cancellation Modules and Homogeneous Idealization

Abstract

All rings are commutative with identity and all modules are unital. In this article, we characterize cancellation modules and use this characterization to give necessary and sufficient conditions for the sum and intersection of cancellation modules to be cancellation. We introduce and give some properties of the concept of join principal submodules. We show that via the method of idealization most questions concerning (weak) cancellation and join principal modules can be reduced to the ideal case.

Key Words:

• Idealization
• ½ Join principal submodule
• Multiplication module
• Projective module
• (Weak) Cancellation module
• ½ (Weak) Cancellation module

2000 Mathematics Subject Classification:

• 13C13
• 13A15

ACKNOWLEDGMENTS

The author is grateful to the referee for helpful suggestions which have resulted in an improvement to the article.

Notes

Communicated by I. Swanson.