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Let    L  := Frm((ℝ),  L ). We show that if  L  is a  P -frame then    L  is an ℵ 0 -self-injective ring. We prove that a zero-dimensional frame  L  is extremally disconnected if and only if    L  is a self-injective ring. Finally, it is shown that    L  is a Baer ring if and only if    L  is a continuous ring if and only if    L  is a complete ring if and only if    L  is a  CS -ring.

On self-injectivity of the f -ring Frm(𝓟(ℝ), L )