Embeddings in division rings
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- by John Dauns PDF
- Trans. Amer. Math. Soc. 150 (1970), 287-299 Request permission
Abstract:
A method for embedding a certain class of integral domains in division rings is devised. Integral domains $A$ are constructed with a generalized valuation into a (noncommutative) totally ordered semigroup that need not be discrete. Then the multiplicative semigroup $A\backslash \{ 0\}$ is expressed as an inverse limit of semigroups each of which is embeddable in a group. Thus $A\backslash \{ 0\}$ can be embedded in a group $G$. The main problem is to introduce addition on $G$ in order that $G$ becomes a division ring by the use of eventually commuting maps of inverse limits.References
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Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 150 (1970), 287-299
- MSC: Primary 16.46
- DOI: https://doi.org/10.1090/S0002-9947-1970-0262291-5
- MathSciNet review: 0262291