A note on embedding a partially ordered ring in a division algebra
HTML articles powered by AMS MathViewer
- by William H. Reynolds
- Proc. Amer. Math. Soc. 37 (1973), 37-41
- DOI: https://doi.org/10.1090/S0002-9939-1973-0306243-3
- PDF | Request permission
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.References
- D. K. Harrison, Finite and infinite primes for rings and fields, Mem. Amer. Math. Soc. 68 (1966), 62. MR 207735
- 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 313302, DOI 10.1090/S0002-9947-1973-0313302-2
- William H. Reynolds, Embedding a partially ordered ring in a division algebra, Trans. Amer. Math. Soc. 158 (1971), 293–300. MR 283026, DOI 10.1090/S0002-9947-1971-0283026-7
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- 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