The Dual of a Strongly Prime Ideal

Author(s):

Reza Jahani , Nezhad

Message:
Abstract:
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^{−1} is a ring. In fact, it is proved that P^{−1} = (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.
Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:5 Issue: 1, May 2010
Page:
19
https://www.magiran.com/p731593