On Projective modules over graded R-subalgebras of R[X,1/X]

2025/06/23 by Garg, Diksha, Gupta, Anjan · 1 citation
#13A02 #13B25 #13C10 #19A13 #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2506.18826

Abstract

Let R be a Noetherian ring of dimension d and A be a graded R-subalgebra of R[X,1/X]. Let P be a projective module over A of rank r ≥ max\d+1,2\ and \v=(a,p) be a unimodular element of A ⊕ P. We find an elementary automorphism τ such that τ(\v) = (1, 0). Consequently, we obtain the cancellative property of P. We show that P splits off a free summand of rank one. When A = R[X] or R[X, 1/ X], the results are well-known due to the contributions by various authors.

Citations

• Subrings of polynomial rings and the conjectures of Eisenbud and Evans
• Unimodular rows over monoid rings
• Some K-theoretic properties of the kernel of a locally nilpotent derivation on k[X₁, …, X₄]
• Equality of Linear and Symplectic Orbits

Cited by

• A generalization of Rao's theorem to graded R-subalgebras of R[t]

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