Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS257269159410.22044/jas.2019.8150.1399ENM.AbediEsfarayen University of Technology, Esfarayen, North Khorasan, Iran.0000-0002-8763-4510Journal Article20190228We study primary ideals of the ring $mathcal{R}L$ of real-valued continuous functions on a completely regular frame $L$. We observe that prime ideals and primary ideals coincide in a $P$-frame. It is shown that every primary ideal in $mathcal{R}L$ is contained in a unique maximal ideal, and an ideal $Q$ in $mathcal{R}L$ is primary if and only if $Q capmathcal{R}^*L$ is a primary ideal in $mathcal{R}^*L$. We show that every pseudo-prime (primary) ideal in $mathcal{R}L$ is either an essential ideal or a maximal ideal which is at the same time a minimal prime ideal. Finally, we prove that if $L$ is a connected frame, then the zero ideal in $mathcal{R}L$ is decomposable if and only if $L={bf2}$.http://jas.shahroodut.ac.ir/article_1594_8108dcd6f42553890dfb9b0ba2055003.pdf