%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