On divided commutative rings. (English) Zbl 0923.13001

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 \(P\).


13A15 Ideals and multiplicative ideal theory in commutative rings
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