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Isomorphisms of Simple Rings
Published online by Cambridge University Press: 20 November 2018
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Let A be a simple ring with minimum condition, and B1, B2, 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 Biσi are regular subrings of A (i = 1, 2), is called compatible if σ1|B1 ∩ B2 = σ2|B1 ∩ B2. Here σ|X means the restriction of σ to X. Bialynicki-Birula has proved some necessary and sufficient conditions that every compatible pair (σ1, σ2) 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 B1 and B2 is necessary and almost sufficient for the existence of a common extension of any compatible pair.
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- Copyright © Canadian Mathematical Society 1963
References
1.
Bialynicki-Birula, Andrzej, Ow automorphisms and derivations of simple rings with minimum condition, Trans. Amer. Math. Soc, 98 (1961), 468–484.Google Scholar
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Rosenberg, Alex and Zelinsky, Daniel, Galois theory of continuous transformation rings, Trans. Amer. Math. Soc, 79 (1955), 429–452.Google Scholar
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