## 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 $$P$$.

### MSC:

 13A15 Ideals and multiplicative ideal theory in commutative rings

### Keywords:

divided ring; zero divisor; divided prime ideal
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### References:

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