# zbMATH — the first resource for mathematics

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