{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T09:29:41Z","timestamp":1772443781602,"version":"3.50.1"},"reference-count":33,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":14802,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1973,9]]},"abstract":"<jats:p>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.<\/jats:p><jats:p>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\u2032.<\/jats:p>","DOI":"10.2307\/2273039","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:24:44Z","timestamp":1146936284000},"page":"428-436","source":"Crossref","is-referenced-by-count":11,"title":["The word problem for division rings"],"prefix":"10.1017","volume":"38","author":[{"given":"Angus","family":"Macintyre","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200054797_ref028","volume-title":"Trudy Matematiceskogo Instituta im V. A. 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