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Paper   IPM / M / 7370
School of Mathematics
  Title:   Catenary, locally equidimensional, and tensor product of algebras
  Author(s): 
1.  S. Yassemi
2.  M. Tousi
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  33
  Year:  2005
  Pages:   1023-1029
  Supported by:  IPM
  Abstract:
In this paper, we show that the property of being catenary and locally equidimensional descends by flat homomorphism. More precisely, if φ: RS is a flat homomorphism of Noetherian rings then S is catenary and equidimensional if R is locally equidimensional and the rings R/\frakpRS, \frakp ∈ MinR, are catenary and locally equidimensional. Let k be a field, A a k-algebra, and K an extension field of k. Then we show that the KkA is universally catenary if one of the following holds:a) A is universally catenary and K a finitely generatedextension field of k.b)A is Noetherian universally catenary and t.d. (K:k) < ∞.c) A is universally catenary and K_kA

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