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 -