RT - Journal Article T1 - The Dual of a Strongly Prime Ideal JF - IJMSI YR - 2010 JO - IJMSI VO - 5 IS - 1 UR - http://ijmsi.ir/article-1-107-en.html SP - 19 EP - 26 K1 - Strongly prime ideal K1 - Divided ideal K1 - Valuation domain. AB - 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^{&minus1} is a ring. In fact, it is proved that P^{&minus1} = (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. LA eng UL http://ijmsi.ir/article-1-107-en.html M3 10.7508/ijmsi.2010.01.003 ER -