Cancellation of projective modules in polynomial rings of prime characteristic

2022/10/31 by Sourjya Banerjee, Banerjee, Sourjya
Mathematics · #13B25 #13C10 #19A13 #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.2210.17337

openalex publication_date 2022/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a commutative Noetherian ring of characteristic p>0, such that dim(A)=d. Let P be a projective A[T₁,...,T_n]-module of rank d. We show that P is cancellative if and only if P/P is cancellative. We deduce some applications. In one of the interesting consequences, we show that the Bass-Quillen conjecture has an affirmative answer in dimension three, when 2 is invertible.

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