2021/04/19 by Maria A. Mathew, Mathew, Maria A., Manoj K. Keshari +1
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2104.09383
openalex publication_date 2021/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a commutative Noetherian ring of dimension d and M a commutative cancellative torsion-free seminormal monoid. Then (1) Let A be a ring of type R[d,m,n] and P be a projective A[M]-module of rank r ≥ max\2,d+1\. Then the action of E(A[M] ⊕ P) on Um(A[M] ⊕ P) is transitive and (2) Assume (R, m, K) is a regular local ring containing a field k such that either char k=0 or char k = p and tr-deg K/\mathbbFp ≥ 1. Let A be a ring of type R[d,m,n]^* and f∈ R be a regular parameter. Then all finitely generated projective modules over A[M], A[M]f and A[M] ⊗R R(T) are free. When M is free both results are due to Keshari and Lokhande.