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Full-Text Articles in Mathematics
Higher Order Z-Ideals In Commutative Rings, Themba Dube, Oghenetega Ighedo
Higher Order Z-Ideals In Commutative Rings, Themba Dube, Oghenetega Ighedo
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study ideals that resemble z-ideals in commutative rings with identity. For each positive integer n, we say an ideal of a commutative ring A is a zn-ideal in case it has the property that if a and b belong to the same maximal ideals of A, and an ϵ I , then bn is also in I. The set of all zn-ideals of A is denoted by A --> ʒn (A). This gives an ascending chain ʒ(A) < ʒ2(A) < ʒ3(A) <… of collections of ideals, starting with the collection of z-ideals. …