Retracts of Laurent polynomial rings
Abstract
Let $R$ be an integral domain and $B=R[x_1,\ldots,x_n]$ be the polynomial ring. In this paper, we consider retracts of $B[1/M]$ for a monomial $M$. We show that (1) if $M=\prod_{i=1}^nx_i$, then every retract is a Laurent polynomial ring over $R$, (2) if $R$ is a perfect field and $n=3$, then every retract is isomorphic to $R[y_1^{\pm1},\ldots,y_s^{\pm1},z_1,\ldots,z_t]$ for some $s,t\geq 0$.
 Publication:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.12681
 arXiv:
 arXiv:2301.12681
 Bibcode:
 2023arXiv230112681N
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 13B25 (Primary);
 14A05 (Secondary)
 EPrint:
 6 pages