Embeddings in division rings

Author:
John Dauns

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

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Abstract: A method for embedding a certain class of integral domains in division rings is devised. Integral domains are constructed with a generalized valuation into a (noncommutative) totally ordered semigroup that need not be discrete. Then the multiplicative semigroup is expressed as an inverse limit of semigroups each of which is embeddable in a group. Thus can be embedded in a group . The main problem is to introduce addition on in order that becomes a division ring by the use of eventually commuting maps of inverse limits.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1970-0262291-5

Keywords:
Integral domain,
division ring,
generalized valuation into a semigroup,
Ore condition,
eventually commuting maps of inverse limits,
P. M. Cohn's embedding theorem,
totally ordered cancellative semigroup,
semigroup congruence

Article copyright:
© Copyright 1970
American Mathematical Society