Some results on pure ideals and trace ideals of projective modules

Abolfazl Tarizadeh

Some results on pure ideals and trace ideals of projective modules

Commutative Algebra 2021-07-14 v2

Authors: Abolfazl Tarizadeh

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.

Keywords

commutative ring pure ideal trace ideal projective module annihilator coordinates

Cite

@article{arxiv.2002.10139,
  title  = {Some results on pure ideals and trace ideals of projective modules},
  author = {Abolfazl Tarizadeh},
  journal= {arXiv preprint arXiv:2002.10139},
  year   = {2021}
}

Comments

9 pages

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