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TENSOR PRODUCTS OF CLEAN RINGS

Published online by Cambridge University Press:  29 November 2005

MASSOUD TOUSI  and
SIAMAK YASSEMI
MASSOUD TOUSI
Affiliation:
Department of Mathematics, Shahid Beheshti University, Tehran, Iran Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran
SIAMAK YASSEMI
Affiliation:
Department of Mathematics, University of Tehran, Tehran, Iran Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran
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Abstract

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A ring is called clean if every element is the sum of an idempotent and a unit. It is an open question whether 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.

Keywords

13A9913F99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 3 , September 2005 , pp. 501 - 503
Copyright
2005 Glasgow Mathematical Journal Trust