On the Extensions of the Cohen Structure Theorem

2024/09/30 by Amartya Goswami, Goswami, Amartya
Computer Science · #13H99 #Advanced Algebra and Logic #Commutative Algebra (math.AC) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2409.20241

openalex publication_date 2024/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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