{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:11:01Z","timestamp":1747195861588},"reference-count":29,"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":1288,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For a finite von Neumann algebra factor <jats:bold>M<\/jats:bold>, the projections form a modular ortholattice <jats:italic>L<\/jats:italic>(<jats:bold>M<\/jats:bold>). We show that the equational theory of <jats:italic>L<\/jats:italic>(<jats:bold>M<\/jats:bold>) coincides with that of some resp. all <jats:italic>L<\/jats:italic>(\u2102<jats:sup>n\u00d7n<\/jats:sup> ) and is decidable. In contrast, the uniform word problem for the variety generated by all <jats:italic>L<\/jats:italic>(\u2102<jats:sup>n\u00d7n<\/jats:sup>) is shown to be undecidable.<\/jats:p>","DOI":"10.2178\/jsl\/1278682219","type":"journal-article","created":{"date-parts":[[2010,7,9]],"date-time":"2010-07-09T13:30:45Z","timestamp":1278682245000},"page":"1102-1110","source":"Crossref","is-referenced-by-count":12,"title":["On the equational theory of projection lattices of finite von neumann factors"],"prefix":"10.1017","volume":"75","author":[{"given":"Christian","family":"Herrmann","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002577_ref029","doi-asserted-by":"crossref","DOI":"10.1090\/memo\/0252","volume-title":"Continuous geometries with a transition probability","author":"von Neumann","year":"1981"},{"key":"S0022481200002577_ref028","volume-title":"Continuous geometry","author":"von Neumann","year":"1960"},{"key":"S0022481200002577_ref026","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1989-044-8"},{"key":"S0022481200002577_ref025","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9026-6"},{"key":"S0022481200002577_ref023","doi-asserted-by":"publisher","DOI":"10.2307\/1968693"},{"key":"S0022481200002577_ref021","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1974-0364040-2"},{"key":"S0022481200002577_ref017","first-page":"41","article-title":"Current interest in orthomodular lattices","author":"Holland","year":"1970","journal-title":"Trends in lattice theory"},{"key":"S0022481200002577_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-005-1853-0"},{"key":"S0022481200002577_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-009-0003-5"},{"key":"S0022481200002577_ref013","first-page":"1194","volume":"72","author":"Hagge","year":"2007","journal-title":"QL(\u2102n) determines n"},{"key":"S0022481200002577_ref011","first-page":"25","article-title":"The word problem for certain classes of semigroups","volume":"5","author":"Gurevich","year":"1966","journal-title":"Algebra and Logic"},{"key":"S0022481200002577_ref009","volume-title":"Von Neumann regular rings","author":"Goodearl","year":"1991"},{"key":"S0022481200002577_ref008","unstructured":"Giudici Luca , Dintorni del teorema di coordinatizatione di von Neumann, Ph.D. thesis. Universita di Milano, 1995."},{"key":"S0022481200002577_ref007","first-page":"353","volume":"70","author":"Dunn","year":"2005","journal-title":"Quantum logic as motivated by quantum computing"},{"key":"S0022481200002577_ref005","doi-asserted-by":"publisher","DOI":"10.2307\/1968621"},{"key":"S0022481200002577_ref004","volume-title":"Lattice theory","author":"Birkhoff","year":"1967"},{"key":"S0022481200002577_ref003","doi-asserted-by":"publisher","DOI":"10.1216\/RMJ-1982-12-1-149"},{"key":"S0022481200002577_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01188384"},{"key":"S0022481200002577_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/1969959"},{"key":"S0022481200002577_ref019","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(73)90001-X"},{"key":"S0022481200002577_ref027","volume-title":"A decision method for elementary algebra and geometry","author":"Tarski","year":"1948"},{"key":"S0022481200002577_ref010","volume-title":"Quadratic forms in infinite-dimensional vector spaces","author":"Gross","year":"1979"},{"key":"S0022481200002577_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8130-3"},{"key":"S0022481200002577_ref024","doi-asserted-by":"publisher","DOI":"10.2307\/1969107"},{"key":"S0022481200002577_ref012","first-page":"184","volume":"49","author":"Gurevich","year":"1984","journal-title":"The word problem for cancellation semigroups with zero"},{"key":"S0022481200002577_ref015","volume-title":"Algebra Universalis","author":"Herrmann","year":"2009"},{"key":"S0022481200002577_ref018","first-page":"297","article-title":"Schwach distributive Verb\u00e4nde I","volume":"33","author":"Huhn","year":"1972","journal-title":"Acta Scientiarum Mathematicarum"},{"key":"S0022481200002577_ref022","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-94727-8"},{"key":"S0022481200002577_ref020","first-page":"562","volume-title":"Collected works of John von Neumann","volume":"III","author":"Kaplansky","year":"1963"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002577","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T21:39:06Z","timestamp":1556401146000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002577\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["S0022481200002577"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1278682219","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9]]}}}