If the longest constraint needs to be flushed to the right margin, you could use a tabular*
environment with two centered columns; something along these lines (change the lengths according to your needs):
\documentclass[reqno]{amsart}
\usepackage{array}
\newlength\MyIndent
\setlength\MyIndent{10em}
\begin{document}
\vspace{\abovedisplayskip}
\noindent\begin{tabular*}{\textwidth}{@{\hspace{\MyIndent}}>{$}c<{$}@{\extracolsep{\fill}}
>{$}c<{$}@{}}
a^2 + b^2 = ab & (a \in \{z,y,x,w,v,u\},\ b \neq 0) \\
a + b = c & (a \in \{z,y\},\ b = 0) \\
\end{tabular*}\par
\vspace{\belowdisplayskip}
\end{document}
If the longest constraint doesn't need to be flushed to the right margin, a simple array environment will do the job (change the lengths according to your needs):
\documentclass[reqno]{amsart}
\begin{document}
\[
\begin{array}{@{\hspace{7em}}c@{\hspace{3em}}c}
a^2 + b^2 = ab & (a \in \{z,y,x,w,v,u\},\ b \neq 0) \\
a + b = c & (a \in \{z,y\},\ b = 0) \\
\end{array}
\]
\end{document}
You can adapt this answer by Andrew Stacey
\documentclass{article}
\usepackage{amsmath}
\makeatletter
\let\reftagform@=\tagform@
\def\tagform@#1{\maketag@@@{(\ignorespaces\textcolor{blue}{#1}\unskip\@@italiccorr)}}
\renewcommand{\eqref}[1]{\textup{\reftagform@{\ref{#1}}}}
\makeatother
\usepackage{hyperref}
\hypersetup{colorlinks=true}
\begin{document}
\begin{equation}
1=\beta\left[ \frac{ 1+\left( 1-\tau_{t+1}\right) r_{t} }{\Pi_{t+1}} \right]\label{Fisher}
\end{equation}
Make reference to \eqref{Fisher}.
\end{document}
Best Answer
Your document
generates an error
After an error you should not really look at the pdf file, TeX makes no attempt to make sensible output, it just recovers to check the rest of the file.
You need
\#
for#
but also multi-letter words should never be set in math italic (which is designed to make them look like a product of variables not a word)actually the error was probably from the blank line:
depending on quite how the original document looked