Badawi, Ayman On divided commutative rings. (English) Zbl 0923.13001 Commun. Algebra 27, No. 3, 1465-1474 (1999). An integral domain \(R\) is said to be divided if so is every prime ideal \(P\) of \(R\) \((P\) is called divided if it is comparable to every principal ideal of \(R)\). In the paper under review, the author generalizes the study of divided domains to the case of commutative unitary rings with zero divisors. Among other results, he shows that a ring \(R\) containing a regular finitely generated divided prime ideal \(P\) is quasi-local with maximal ideal \(P\). Reviewer: Tiberiu Dumitrescu (Bucureşti) Cited in 4 ReviewsCited in 54 Documents MSC: 13A15 Ideals and multiplicative ideal theory in commutative rings Keywords:divided ring; zero divisor; divided prime ideal × 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., Lecture Notes Pure Appl. Math 171 pp 151– (1995) [5] DOI: 10.1080/00927879508825469 · Zbl 0843.13007 · doi:10.1080/00927879508825469 [6] Badawi, A., Anderson, D.F. and Dobbs, D.E. Pseudovaluation rings. Proceedings of The Second International Conference On Commutative Rings. Vol. 185, pp.57–67. Basel, New York: Marcel Dekker. Lecture Notes Pure Appl. Math · Zbl 0880.13011 [7] DOI: 10.1080/00927879808826164 · Zbl 0919.13004 · doi:10.1080/00927879808826164 [8] Dobbs D.E., Pacific J. Math 67 pp 353– (1976) [9] Dobbs D.E., Lecture Notes Pure Appl. Math 189 pp 305– (1997) [10] Kaplansky I., Commutative Rings (1974) 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.