Abstract
We prove that every -module has an indecomposable decomposition. As an immediate consequence, every -module M with the finite exchange is clean and has the full exchange. Moreover, in this case the module M admits an indecomposable decomposition with each Mi having local endomorphism ring, and the decomposition complements direct summands.
2010 Mathematics Subject Classification:
Acknowledgements
The second author would like to acknowledge the support received from the Ohio State University at Lima in the form of a research leave during the spring semester of 2019.