Title of article :
Sums of Strongly z-Ideals and Prime Ideals in RL
Author/Authors :
Estaji, A.A. Faculty of Mathematics and Computer Sciences - Hakim Sabzevari University, Sabzevar, Iran , Karimi Feizabadi, A. Department of Mathematics - Islamic Azad University Gorgan Branch, Gorgan, Iran , Robat Sarpoushi, M. Faculty of Mathematics and Computer Sciences - Hakim Sabzevari University, Sabzevar, Iran
Abstract :
It is well known that the sum of two z-ideals in C(X) is either
C(X) or a z-ideal. The main aim of this paper is to study the sum of
strongly z-ideals in RL, the ring of real-valued continuous functions on
a frame L. For every ideal I in RL, we introduce the biggest strongly z-
ideal included in I and the smallest strongly z-ideal containing I, denoted
by Isz and Isz, respectively. We study some properties of Isz and Isz:
Also, it is observed that the sum of any family of minimal prime ideals in
the ring RL is either RL or a prime strongly z-ideal in RL. In particular,
we show that the sum of two prime ideals in RL which are not chains is
a prime strongly z-ideal.
Keywords :
Frame , Ring of real-valued continuous functions , z-Ideal , Strongly z-ideal
Journal title :
Iranian Journal of Mathematical Sciences and Informatics (IJMSI)
