on primary ideals of pointfree function rings

We study primary ideals of the ring rl 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 rl is contained in a unique maximal ideal, and an ideal q in rl is primary if and only if q ∩ r∗l is a primary ideal in r∗l. we show that every pseudo-prime (primary) ideal in rl 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 rl is decomposable if and only if l = 2.