Oka and Ako Ideal Families in Commutative Rings
نویسندگان
چکیده
In our earlier study [LR] of prime ideal principles in commutative rings, we have introduced the notion of Oka and Ako families of ideals, along with their “strong analogues”. The logical hierarchy between these ideal families (and the classically well-known monoidal families of ideals) was partly worked out in [LR] over general commutative rings. In the present paper, we amplify this study by developing further hierarchical relationships among these families over special classes of rings, and also by finding concrete examples of ideal families to show that certain such relationships cannot be reversed or improved. The special types of commutative rings studied here include von Neumann regular rings and integral domains (for instance Dedekind domains and valuation domains).
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