Year: 2025
Type: preprint
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 $r \geq \max\{d+1,2\}$ and $\v=(a,p)$ be a unimodular element of $A \oplus P$. 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.
Source: arXiv (Cornell University)
Authors: Garg, Diksha, Gupta, Anjan
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979363893
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