Nonstandard polynomials: algebraic properties and elementary equivalence
Nonstandard polynomials: algebraic properties and elementary equivalence
We solve the first-order classification problem for rings $R$ of polynomials $F[x_1, \ldots,x_n]$ and Laurent polynomials $F[x_1,x_1^{-1}, \ldots,x_n,x_n^{-1}]$ with coefficients in an infinite field $F$ or the ring of integers $\mathbb Z$, that is, we describe the algebraic structure of all rings $S$ that are first-order equivalent to $R$. Our …