Badawi, Ayman On domains which have prime ideals that are linearly ordered. (English) Zbl 0843.13007 Commun. Algebra 23, No. 12, 4365-4373 (1995). It is well-known that a GCD domain \(R\) in which the set of prime ideals are linearly ordered is a valuation ring. The purpose of the paper is to provide an alternative proof of this fact. Furthermore, a characterizations of divided domains and of pseudo-valuation domains are given. Reviewer: K.Koh (Raleigh) Cited in 19 Documents MSC: 13G05 Integral domains 13F30 Valuation rings Keywords:divided domain; pseudo-valuation domain; GCD domain; valuation ring × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Anderson D.F., Houston J. Math 5 pp 451– (1979) [2] Anderson D.F., Houston J. Math 9 pp 325– (1983) [3] DOI: 10.4153/CJM-1980-029-2 · Zbl 0406.13001 · doi:10.4153/CJM-1980-029-2 [4] Badawi, A. 1995. ”A Visit to valuation and pseudo-valuation domains”. Vol. 171, 155–161. Marcel Dekker, Inc. Zero-dimensional commutative rings · Zbl 0885.13015 [5] DOI: 10.4153/CJM-1974-017-9 · Zbl 0242.13015 · doi:10.4153/CJM-1974-017-9 [6] Dobbs D.E., Pacific J.Math 67 pp 253– (1976) [7] Hedstrom J.R., Pacific J. Math 4 pp 199– (1978) [8] Kaplansky, I. 1974. ”Commutative rings”. Chicago: The Univ. of Chicago Press. [9] DOI: 10.1016/0021-8693(72)90128-7 · Zbl 0254.13009 · doi:10.1016/0021-8693(72)90128-7 [10] DOI: 10.4153/CJM-1974-010-8 · Zbl 0247.13009 · doi:10.4153/CJM-1974-010-8 [11] DOI: 10.1090/S0002-9939-1972-0308115-6 · doi:10.1090/S0002-9939-1972-0308115-6 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.