Geometric characterization of flat modules

Carlos Sancho; Fernando Sancho; Pedro Sancho

Geometric characterization of flat modules

Algebraic Geometry 2017-10-12 v5 Commutative Algebra

Authors: Carlos Sancho , Fernando Sancho , Pedro Sancho

Abstract

Let $R$ be a commutative ring. Roughly speaking, we prove that an $R$ -module $M$ is flat iff it is a direct limit of $R$ -module affine algebraic varieties, and $M$ is a flat Mittag-Leffler module iff it is the union of its $R$ -submodule affine algebraic varieties.

Keywords

module theory affine algebraic geometry lie algebras and modules

Cite

@article{arxiv.1609.08327,
  title  = {Geometric characterization of flat modules},
  author = {Carlos Sancho and Fernando Sancho and Pedro Sancho},
  journal= {arXiv preprint arXiv:1609.08327},
  year   = {2017}
}

Comments

27 pages

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