English

On the Extensions of the Cohen Structure Theorem

Commutative Algebra 2024-10-01 v1

Abstract

The purpose of this note is to pose a question that, when answered, would directly imply the Cohen Structure Theorem. We provide a solution to this question for a specific class of local rings (not necessarily complete). We also explore how this question connects to the Gelfand-Mazur Theorem and, more broadly, to a fundamental theorem in Gelfand theory. Finally, we provide a categorical reformulation of the question.

Keywords

Cite

@article{arxiv.2409.20241,
  title  = {On the Extensions of the Cohen Structure Theorem},
  author = {Amartya Goswami},
  journal= {arXiv preprint arXiv:2409.20241},
  year   = {2024}
}