%0 Journal Article %A Jahani-Nezhad, Reza %T The Dual of a Strongly Prime Ideal %J Iranian Journal of Mathematical Sciences and Informatics %V 5 %N 1 %U http://ijmsi.ir/article-1-107-en.html %R 10.7508/ijmsi.2010.01.003 %D 2010 %K Strongly prime ideal, Divided ideal, Valuation domain., %X 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. %> http://ijmsi.ir/article-1-107-en.pdf %P 19-26 %& 19 %! %9 Research paper %L A-10-1-76 %+ %G eng %@ 1735-4463 %[ 2010