On the inheritance of the strongly π-extending property

ABSTRACT

In this article, we focus on modules with the property that every projection invariant submodule is essential in a fully invariant direct summand. In contrast to π-extending condition, it is shown that the former property is inherited by direct summands and Morita invariant. An application of our results yields that the endomorphism ring of a free module enjoys the property. Moreover, we characterize generalized triangular matrix rings with the aforementioned property and apply to somewhat special cases.

KEYWORDS:

• Endomorphsim ring
• π-extending module
• generalized triangular matrix ring
• projection invariant

2010 AMS SUBJECT CLASSIFICATION:

• Primary: 16D10
• 16D50
• Secondary: 16D40

View correction statement:

Corrigendum to: on the inheritance of the strongly π-extending property

Acknowledgment

The authors are grateful to Professor Dr. Gary F. Birkenmeier for his encouragement during the preparation of this paper. Besides the authors would like to express their appreciation to the referee for his/her helpful comments which improve the paper.