Generalizing Serre's Splitting Theorem and Bass's Cancellation Theorem via free-basic elements

2016/08/30 by Alessandro De Stefani, De Stefani, Alessandro, Thomas Polstra +3 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1608.08591

openalex publication_date 2016/08/30 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

Abstract

We give new proofs of two results of Stafford, which generalize two famous Theorems of Serre and Bass regarding projective modules. Our techniques are inspired by the theory of basic elements. Using these methods we further generalize Serre's Splitting Theorem by imposing a condition to the splitting maps, which has an application to the case of Cartier algebras.

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• Surjective and splitting capacities

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