Embedding rings with a maximal cone and rings with an involution in quaternion algebras
Authors:
Carl W. Kohls and William H. Reynolds
Journal:
Trans. Amer. Math. Soc. 176 (1973), 411419
MSC:
Primary 16A28; Secondary 06A70, 46K99
MathSciNet review:
0313302
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Abstract: Sufficient conditions are given for an algebra over a totally ordered field F to be isomorphic to a subring of the algebra of quaternions over the real closure of F. These conditions include either the requirement that the nonnegative scalars form a maximal cone in the algebra, or that the algebra have an involution such that the scalars are the only symmetric elements. For many matrix algebras, the cone requirement alone is imposed.
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 D. K. Harrison, Finite and infinite primes for rings and fields, Mem. Amer. Math. Soc. No. 68 (1966). MR 34 #7550. MR 0207735 (34:7550)
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 I. N. Herstein and Susan Montgomery, A note on division rings with involutions, Michigan Math. J. 18 (1971), 7579. MR 44 #250. MR 0283017 (44:250)
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 D. G. Northcott, An introduction to homological algebra, Cambridge Univ. Press, New York, 1960. MR 22 #9523. MR 0118752 (22:9523)
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 R. S. Palais, The classification of real division algebras, Amer. Math. Monthly 75 (1968), 366368. MR 37 #4119. MR 0228539 (37:4119)
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 W. H. Reynolds, Embedding a partially ordered ring in a division algebra, Trans. Amer. Math. Soc. 158 (1971), 293300. MR 44 #259. MR 0283026 (44:259)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197303133022
PII:
S 00029947(1973)03133022
Article copyright:
© Copyright 1973
American Mathematical Society
