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The word problem for division rings

Published online by Cambridge University Press:  12 March 2014

Angus Macintyre
Angus Macintyre*
Affiliation:
King's College, Old Aberdeen, Scotland
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Extract

In this paper we prove that the word problem for division rings is recursively unsolvable. Our proof relies on the corresponding result for groups [7], [28], and makes essential use of P. M. Cohn's recent work [11], [13], [15], [16] on division rings.

The word problem for groups is usually formulated in terms of group presentations or finitely presented groups, as in [7], [24], [28], [30]. An equivalent formulation, in terms of the universal Horn sentences of group theory, is mentioned in [32]. This formulation makes sense for arbitrary first-order theories, and it is with respect to this formulation that we show that the word problem for division rings has degree 0′.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 38 , Issue 3 , September 1973 , pp. 428 - 436
Copyright
Copyright © Association for Symbolic Logic 1973

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References

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