The primarily finite property in polynomial and power series rings over a pseudo-valuation domain

초록

We show that if D is a pseudo-valuation domain, then D[X] and D[[X]] are primarily finite rings. We also show that for ≥2 and for a pseudo-valuation domain D with proper associated valuation domain V and maximal ideal m, ⁡[1,…,] (resp., ⁡[[1,…,]]) is a primarily finite ring if and only if ⁡[1,…,] (resp., ⁡[[1,…,]]) is a primarily finite ring and m is a finitely generated ideal of D.

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