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| Paper IPM / M / 7370 |
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| Abstract: | |||||
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In this paper, we show that the property of being
catenary and locally equidimensional descends by flat
homomorphism. More precisely, if φ: R → S is a
flat homomorphism of Noetherian rings then S is catenary and
equidimensional if R is locally equidimensional and the rings
R/\frakp⊗RS, \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
K⊗kA 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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