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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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), 411-419
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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DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0313302-2
PII: S 0002-9947(1973)0313302-2
Article copyright: © Copyright 1973 American Mathematical Society