Power series over generalized Krull domains

TL;DR

This paper investigates whether the formal power series ring over a generalized Krull domain retains the same algebraic property, and concludes that it does not, resolving an open problem in the field.

Contribution

The paper provides a definitive answer to an open question by demonstrating that R[[X]] is not a generalized Krull domain when R is, clarifying the behavior of power series rings in this context.

Findings

R[[X]] is not a generalized Krull domain if R is a generalized Krull domain.

The result resolves a previously open problem posed by Jarden.

The study advances understanding of the structure of power series rings over special classes of domains.

Abstract

We resolve an open problem in commutative algebra and Field Arithmetic, posed by Jarden -- Let R be a generalized Krull domain. Is the ring R[[X]] of formal power series over R a generalized Krull domain? We show that the answer is negative.