{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:06:55Z","timestamp":1773814015568,"version":"3.50.1"},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":13068,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1978,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>n<\/jats:italic> \u2265 3. The following theorems are proved.<\/jats:p><jats:p>Theorem. <jats:italic>The theory of the class of strictly upper triangular n<\/jats:italic> \u00d7 <jats:italic>n matrix rings over fields is finitely axiomatizable<\/jats:italic>.<\/jats:p><jats:p>Theorem. <jats:italic>If R is a strictly upper triangular n<\/jats:italic> \u00d7 <jats:italic>n matrix ring over a field K, then there is a recursive map \u03c3 from sentences in the language of rings with constants for K into sentences in the language of rings with constants for R such that K<\/jats:italic> \u22a8 \u03c6 <jats:italic>if and only if R<\/jats:italic> \u03c6 \u03c3(\u03c6).<\/jats:p><jats:p>Theorem. <jats:italic>The theory of a strictly upper triangular n<\/jats:italic> \u00d7 <jats:italic>n matrix ring over an algebraically closed field is<\/jats:italic> \u2135<jats:sub>1<\/jats:sub>-<jats:italic>categorical<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2272823","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:47:35Z","timestamp":1146937655000},"page":"250-259","source":"Crossref","is-referenced-by-count":4,"title":["The \u2135<sub>1<\/sub>-categoricity of strictly upper triangular matrix rings over algebraically closed fields"],"prefix":"10.1017","volume":"43","author":[{"given":"Bruce I.","family":"Rose","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200049598_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771574"},{"key":"S0022481200049598_ref005","doi-asserted-by":"publisher","DOI":"10.4064\/fm-71-1-1-25"},{"key":"S0022481200049598_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(76)90017-6"},{"key":"S0022481200049598_ref001","volume-title":"Model theory","author":"Chang","year":"1972"},{"key":"S0022481200049598_ref003","doi-asserted-by":"publisher","DOI":"10.4064\/fm-82-4-331-346"},{"key":"S0022481200049598_ref007","volume-title":"Saturated model theory","author":"Sacks","year":"1972"},{"key":"S0022481200049598_ref004","doi-asserted-by":"publisher","DOI":"10.4064\/fm-70-3-253-270"},{"key":"S0022481200049598_ref006","first-page":"124","volume-title":"A. I. Mal'cev, The metamathematics of algebraic systems","author":"Mal'cev","year":"1971"},{"key":"S0022481200049598_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01463149"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200049598","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T15:57:49Z","timestamp":1558972669000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200049598\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,6]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1978,6]]}},"alternative-id":["S0022481200049598"],"URL":"https:\/\/doi.org\/10.2307\/2272823","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,6]]}}}