Some results on pure ideals and trace ideals of projective modules

Abolfazl Tarizadeh

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arXiv · 2002.10139

Some results on pure ideals and trace ideals of projective modules

Abolfazl Tarizadeh

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Abstract

Let $R$ be a commutative ring with the unit element. It is shown that an ideal $I$ in $R$ is pure if and only if Ann$(f)+I=R$ for all $f\in I$. If $J$ is the trace of a projective $R$-module $M$, we prove that $J$ is generated by the ``coordinates" of $M$ and $JM = M$. These lead to a few new results and alternative proofs for some known results.

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Abolfazl Tarizadeh. 2020-02-24. Some results on pure ideals and trace ideals of projective modules. https://arxiv.org/abs/2002.10139

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