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Paper   IPM / M / 8026
School of Mathematics
  Title:   Tensor products of clean rings
  Author(s): 
1.  M. Tousi
2.  S. Yassemi
  Status:   Published
  Journal: Glasgow Math. J.
  Vol.:  47
  Year:  2005
  Pages:   501-503
  Supported by:  IPM
  Abstract:
A ring is called 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.


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