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On Mori domains and commutative rings with \(CC^{\perp}\). II. (English) Zbl 0711.13006
This paper is a sequel to part I [ibid. 56, No.3, 247-268 (1989; Zbl 0677.13005)]. A commutative domain A is Mori if and only if it satisfies the ascending chain condition on divisorial ideals (so that e.g. a domain A is Krull if and only if it is Mori and completely integrally closed). The main result here is the construction of a Mori domain A such that A[[X]] is not Mori, thus confirming a conjecture by P. Ribenboim [“Power series over Mori domains”, Queen’s Univ. Prepr. No.21 (1986); see also Commun. Algebra 16, No.5, 1017-1026 (1988; Zbl 0699.13009)]. Some further results and examples concerning finitely generated over- rings and pullbacks of Mori domains are also included.
Reviewer: K.A.Brown

13E15 Commutative rings and modules of finite generation or presentation; number of generators
13B25 Polynomials over commutative rings
Full Text: DOI
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