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arXiv · 2109.14043

The nilpotency of the prime radical of a Goldie module

John A. Beachy·Mauricio Medina-Bárcenas
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Abstract

With the notion of prime submodule defined by F. Raggi et.al. we prove that the intersection of all prime submodules of a Goldie module $M$, is a nilpotent submodule provided that $M$ is retractable and $M^{(\Lambda)}$-projective for every index set $\Lambda$. This extends the well known fact that in a left Goldie ring, the prime radical is nilpotent.

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John A. Beachy, Mauricio Medina-Bárcenas. 2021-09-28. The nilpotency of the prime radical of a Goldie module. https://arxiv.org/abs/2109.14043

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