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Un exemple d’anneau caténaire. (An example of a catenarian ring). (English) Zbl 0664.13008
Let \({\mathbb{Z}}_{(2)}[[ X]]\) be the ring of formal power series over \({\mathbb{Z}}_{(2)}\) and K its quotient field. Let \(T={\mathbb{Z}}_{(2)}[[ X]]+YK[[ Y]]\) be the subring of \(K[[ Y]]\) made up of series whose constant terms are in \({\mathbb{Z}}_{(2)}[[ X]]\). The author shows that T is a non-Noether, non-Prüfer ring of dimension 3 such that \(T[[ Z]]\) is a catenarian ring of dimension 4.
MSC:
13F25 Formal power series rings
13E99 Chain conditions, finiteness conditions in commutative ring theory
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