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Proceedings of the American Mathematical Society

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A note on embedding a partially ordered ring in a division algebra


Author: William H. Reynolds
Journal: Proc. Amer. Math. Soc. 37 (1973), 37-41
MSC: Primary 16A08
DOI: https://doi.org/10.1090/S0002-9939-1973-0306243-3
MathSciNet review: 0306243
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Abstract: If H is a maximal cone of a ring A such that the subring generated by H is a commutative integral domain that satisfies a certain centrality condition in A, then there exist a maximal cone $ H'$ in a division ring $ A'$ and an order preserving monomorphism of A into $ A'$, where the subring of $ A'$ generated by $ H'$ is a subfield over which $ A'$ is algebraic. Hypotheses are strengthened so that the main theorems of the author's earlier paper hold for maximal cones.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0306243-3
Keywords: Partially ordered ring, maximal cone, order preserving monomorphism, algebraic division algebra
Article copyright: © Copyright 1973 American Mathematical Society

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