Let A be a simple ring with minimum condition, and B 1, B 2, and C be regular subrings of A such that Bi > C, i = 1, 2. A pair of isomorphisms σi of Bi into A such that σi|C is the identity, and that Bi σi are regular subrings of A (i = 1, 2), is called compatible if σ1|B 1 ∩ B 2 = σ2|B 1 ∩ B 2. Here σ|X means the restriction of σ to X. Bialynicki-Birula has proved some necessary and sufficient conditions that every compatible pair (σ 1, σ 2) has a common extention to an automorphism σ of A (1 ). When A is a division ring, he shows that the linear disjointness of the division subrings B 1 and B 2 is necessary and almost sufficient for the existence of a common extension of any compatible pair.