An element x of a ring R is said to be a zero divisor if xy = 0 for some nonzero element of R. Let I be a nonzero ideal of R. The dual of I is the set I-1. Extensive research has been done on duals of ideals and trace properties of ideals in domains. Our work will focus on the stability of these results in rings with zero divisors. Attention will be given to when duals of radical ideals are rings. We will prove several new results including, if R is RTP and I is a finitely generated noninvertible ideal of R then IS(I) = S(I) where S(I) is the ideal transform of I. We also will show the equivalence of RTP, TPP, and LTP in rings with zero divisors. Furthermore, we will focus on sharp properties and properties of prime ideals in strong Prufer rings.
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