Let L  be a frame. We denoted the set of all regular ideals of cozL by rId(cozL) . The aim of this paper is to study these ideals. For a  frame L , we show that  rId(cozL) is a compact completely regular frame and the map j_c : rId(cozL)→L  given by j_c (I)=⋁I   is a compactification of L which is isomorphism to its  Stone–Čech compactification and is proved that j_c have a right adjoint r_c : L → rId(cozL) , given by r_c(a)={x∈cozL : x≺≺a}. Moreover we identify prime and compact elements of rId(cozL) and we investigate the relation between regular ideals of cozL and P-frames. In addition it is shown that  a  frame L  is a P-frame if and only if any ideal of cozL is regular../files/site1/files/51/%D8%B9%D8%A7%D8%A8%D8%AF%DB%8C.pdf