Some results on retracts of polynomial rings

2019/10/24 by Chakraborty, Sagnik, Dasgupta, Nikhilesh, Dutta, Amartya Kumar +1
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.11023

Abstract

In this paper, we first consider the relationship between a polynomial ring B over a Noetherian domain R and the ring of invariants A of a \mathbb G_a-action on B, when A occurs as a retract of B. Next, we study retracts of a polynomial ring in general and address the questions of D. L. Costa raised in \citeC. Finally, we examine the behaviour of ideals and certain properties of rings under retractions.

Related

• Monomial retracts of polynomial rings are polynomial rings
• Remarks on retracts of polynomial rings in three variables in any characteristic
• Coordinates, retracts and automorphisms
• Retracts of Laurent polynomial rings
• Polynomial Retracts and the Jacobian Conjecture