Existence of unimodular element in a projective module over symbolic Rees algebras

Chandan Bhaumik; Husney Parvez Sarwar

doi:10.1007/s12044-023-00768-w

Existence of unimodular element in a projective module over symbolic Rees algebras

Commutative Algebra 2024-02-26 v1

Authors: Chandan Bhaumik , Husney Parvez Sarwar

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Abstract

Let $A$ be a symbolic (or an extended symbolic) Rees algebra (need not be Noetherian) of dimension $d$ . Let $P$ be a finitely generated projective $A$ -module of rank $\geq$ $d$ . Then P has a unimodular element. This improves the classical result of Serre for the mentioned class of algebras.

Keywords

unimodular element projective module symbolic Rees algebra Serre's theorem commutative algebra

Cite

@article{arxiv.2301.05394,
  title  = {Existence of unimodular element in a projective module over symbolic Rees algebras},
  author = {Chandan Bhaumik and Husney Parvez Sarwar},
  journal= {arXiv preprint arXiv:2301.05394},
  year   = {2024}
}

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