Remarks on retracts of polynomial rings in three variables in any characteristic

2024/12/18 by Kojima, Hideo, Nagamine, Takanori, Sasagawa, Riko
#13A50 #13B25 #13N15 #14R20 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.13424

Abstract

Let A be a retract of the polynomial ring in three variables over a field k. It is known that if \rm char (k) = 0 or \rm tr.deg _k A \not= 2 then A is a polynomial ring. In this paper, we give some sufficient conditions for A to be the polynomial ring in two variables over k when \rm char (k) > 0 and \rm tr.deg _k A = 2.

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