TY - JOUR
T1 - The Dual of a Strongly Prime Ideal
TT -
JF - IJMSI
JO - IJMSI
VL - 5
IS - 1
UR - http://ijmsi.ir/article-1-107-en.html
Y1 - 2010
SP - 19
EP - 26
KW - Strongly prime ideal
KW - Divided ideal
KW - Valuation domain.
N2 - 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.
M3 10.7508/ijmsi.2010.01.003
ER -