Is it possible to get a new line in \{text bla bla text\}?

Question

Is it possible to get a new line inside of {text bla bla text} in LaTeX, specifically in mathmode?

I want to be able to write something like this:

Answer 1

Maybe something like this?

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{equation*}
  \left\{
    \begin{matrix}
      \text{Ideals of} \\
      \mathbb{K}\{\alpha_1,\ldots,\alpha_n\} \\
    \end{matrix}
  \right\}
  \begin{matrix}
    \xrightarrow{\mskip50mu \smash{Z} \mskip50mu} \\
    \xleftarrow{\mskip50mu \smash{I} \mskip50mu} \\
  \end{matrix}
  \left\{
    \begin{matrix}
      \text{subsets of } \mathbb{A}^n \\
      \\
    \end{matrix}
  \right\}
\end{equation*}
\end{document}

Answer 2

I suggest tikz-cd:

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{tikz-cd}
\begin{document}
[
\begin{tikzcd}[column sep=huge]
\biggl{
  \begin{tabular}{@{}c@{}}
  Ideals of \ $\mathbb{K}[\alpha_1,\dots,\alpha_n]$
  \end{tabular}
\biggr}
\arrow[r,shift left=1ex,"Z"]
&
\biggl{
  \begin{tabular}{@{}c@{}}
  Subsets of $\mathbb{A}^n$
  \end{tabular}
\biggr}
\arrow[l,shift left=1ex,"I"]
\end{tikzcd}
]
\end{document}

You really want I underneath the arrow, in order to avoid ambiguity.

Answer 3

Or like this ...

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{mathtools}
\begin{document}
\[\Bigg\{\begin{array}{c}
\text{Ideals of}\\
\mathbb{K}[\alpha_{1},\dots,\alpha_{n}]
\end{array}\Bigg\} 
\xleftrightharpoons[~~~~I~~~~]{Z}
\Bigg\{ \begin{array}{c}
\text{subsets of}\ \mathbb{A}^{n}
\end{array}
\Bigg\}\]
\end{document}