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

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 in a division ring and an order preserving monomorphism of *A* into , where the subring of generated by is a subfield over which is algebraic. Hypotheses are strengthened so that the main theorems of the author's earlier paper hold for maximal cones.

**[1]**D. K. Harrison,*Finite and infinite primes for rings and fields*, Mem. Amer. Math. Soc. No.**68**(1966), 62. MR**0207735****[2]**Carl W. Kohls and William H. Reynolds,*Embedding rings with a maximal cone and rings with an involution in quaternion algebras*, Trans. Amer. Math. Soc.**176**(1973), 411–419. MR**0313302**, 10.1090/S0002-9947-1973-0313302-2**[3]**William H. Reynolds,*Embedding a partially ordered ring in a division algebra*, Trans. Amer. Math. Soc.**158**(1971), 293–300. MR**0283026**, 10.1090/S0002-9947-1971-0283026-7

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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