Monomial retracts of polynomial rings are polynomial rings

2025/04/19 by Chakraborty, Sagnik, Pal, Madhuparna
#13B25 #14A05 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.14382

Abstract

Let R be a ring and B = R[X₁, …, X_n] the polynomial ring in n variables over R. In this article, we consider retractions φ: B \longrightarrow B such that φ(X_i) is either a monic monomial or 0. We prove that if R is an integral domain, then any such retract is isomorphic to R^[p], the polynomial ring in p variables over R, for some 0 ≤ p ≤ n. We also characterize different monomial retractions of B which give the same retract.

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