\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
A ring is called {\it clean} if every element is the sum of an
idempotent and a unit. It is an open question wether the tensor
products of two clean algebras over a field is clean. In this note
we study the tensor product of clean algebras over a field and we
provide some examples to show that the tensor product of two clean
algebras over a field need not be clean.
\end{document}