# Baer's lower nilradical and classical prime submodules

Document Type : Research Paper

Authors

1 Abant İzzet Baysal University

2 Istanbul Technical University

Abstract

Let $N$ be a submodule of a module $M$ and a minimal primary decomposition of $N$ is known‎. ‎A formula to compute Baer's lower nilradical of $N$ is given‎. ‎The relations between classical prime submodules and their nilradicals are investigated‎. ‎Some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

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### History

• Receive Date: 08 December 2012
• Revise Date: 20 September 2013
• Accept Date: 20 September 2013