Abstract
We give necessary and sufficient conditions for the power series ring $${R{[[x_1,\ldots,x_n]]}}$$ to be a Jaffard domain, where R is an almost pseudo-valuation domain.
Highlights
All rings considered below are (commutative with identity) integral domains. The dimension of a ring R, denoted by dim R, means its Krull dimension
All rings considered below are integral domains
We are interested in when the power series ring R[[x]] is a Jaffard domain
Summary
All rings considered below are (commutative with identity) integral domains. The dimension of a ring R, denoted by dim R, means its Krull dimension. Recall that an integral domain R is a GPVD [6] if there exists a Prüfer overring T of R such that (i) R ⊆ T is a unibranched extension, and (ii) there exists a nonzero radical ideal I common to T and R such that the rings T /I and R/I are zero-dimensional.
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