On the structure of Goldie modules

ABSTRACT

Let M be a semiprime Goldie module which is projective in σ[M]. We give several decompositions of the M-injective hull $\hat{M}$ of M in terms of its minimal prime submodules. Then, we use this to give a decomposition of the endomorphism ring of $\hat{M}$. We also show that the set of minimal primes of M is in bijective correspondence with the set of isomorphism classes of simple modules over ${End}_R\left(\hat{M}\right)$. We also investigate the relationships between semiprime Goldie modules, QI-modules and co-semisimple modules. As an application we extend certain results on left QI-rings and V-rings.

KEYWORDS:

• Goldie module
• prime module
• semiprime module

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16D50
• 16D80
• 16P50
• 16P70

Acknowledgments

The authors are very thankful to the referee for his/her thorough report on the paper and useful suggestions to improve the presentation.