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Let R be a commutative integral domain with quotient field K and let P be a nonzero STRONGLY PRIME IDEAL of R. We give several characterizations of such ideals. It is shown that (P: P) is a VALUATION DOMAIN with the unique maximal ideal P. We also study when P-1 is a ring. In fact, it is proved that P-1=(P: P) if and only if P is not invertible. Furthermore, if P is invertible, then R=(P: P) and P is a principal ideal of R.