2024/05/27 by Chandan Bhaumik, Bhaumik, Chandan, Md Abu Raihan +3
Mathematics · #19A15 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13C10 #Rings, Modules, and Algebras #Secondary 19A13
paper · pdf · doi:10.48550/arxiv.2405.17096
openalex publication_date 2024/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a Rees-like algebra of dimension d and N a commutative partially cancellative torsion-free seminormal monoid. We prove the following results. \beginenumerate \item Let P be a finitely generated projective A-module of \rank≥ d. Then (i) P has a unimodular element; (ii) The action of \EL(A⊕ P) on \Um(A⊕ P) is transitive. \item Let P be a finitely generated projective A[N]-module of \rank~r. Then (i) P has a unimodular element for r≥max\3,d\; (ii) The action of \EL(A[N]⊕ P) on \Um(A[N]⊕ P) is transitive for r≥max\2,d\. \endenumerate These improve the classical results of Serre \citeSe58 and Bass \citeBa64.