{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T21:28:34Z","timestamp":1648848514798},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2018,3,24]],"date-time":"2018-03-24T00:00:00Z","timestamp":1521849600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2019,3]]},"DOI":"10.1007\/s00500-018-3157-2","type":"journal-article","created":{"date-parts":[[2018,3,24]],"date-time":"2018-03-24T07:18:22Z","timestamp":1521875902000},"page":"1465-1475","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A semiring-like representation of lattice pseudoeffect algebras"],"prefix":"10.1007","volume":"23","author":[{"given":"Ivan","family":"Chajda","sequence":"first","affiliation":[]},{"given":"Davide","family":"Fazio","sequence":"additional","affiliation":[]},{"given":"Antonio","family":"Ledda","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,3,24]]},"reference":[{"issue":"1","key":"3157_CR1","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/s11083-011-9234-0","volume":"30","author":"LP Belluce","year":"2013","unstructured":"Belluce LP, Di Nola A, Ferraioli AR (2013) MV-semirings and their sheaf representations. Order 30(1):165\u2013179","journal-title":"Order"},{"key":"3157_CR2","volume-title":"Orthomodular lattices: an algebraic approach. Mathematics and its applications","author":"L Beran","year":"2011","unstructured":"Beran L (2011) Orthomodular lattices: an algebraic approach. Mathematics and its applications. Springer, Netherlands"},{"issue":"5","key":"3157_CR3","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1093\/jigpal\/jzw031","volume":"24","author":"S Bonzio","year":"2016","unstructured":"Bonzio S, Chajda I, Ledda A (2016) Representing quantum structures as near semirings. Logic J IGPL 24(5):719\u2013742","journal-title":"Logic J IGPL"},{"key":"3157_CR4","unstructured":"Chajda I (2012) Basic algebras and their applications. An overview. In: Czermak J et al (eds) Proceedings of 81st workshop on general algebra, Salzburg, Austria, 2011. Johannes Heyn, Klagenfurt, pp 1\u201310"},{"key":"3157_CR5","doi-asserted-by":"publisher","first-page":"1129","DOI":"10.1007\/s00500-014-1537-9","volume":"19","author":"I Chajda","year":"2015","unstructured":"Chajda I, L\u00e4nger H (2015) Commutative basic algebras and coupled near semirings. Soft Comput 19:1129\u20131134","journal-title":"Soft Comput"},{"key":"3157_CR6","doi-asserted-by":"publisher","first-page":"3719","DOI":"10.1007\/s10773-016-3191-8","volume":"56","author":"I Chajda","year":"2017","unstructured":"Chajda I, L\u00e4nger H (2017) A representation of lattice effect algebras by means of right near semirings with involution. Int J Theor Phys 56:3719\u20133726","journal-title":"Int J Theor Phys"},{"key":"3157_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0526-4","volume-title":"Reasoning in quantum theory: sharp and unsharp quantum logic","author":"ML Dalla Chiara","year":"2004","unstructured":"Dalla Chiara ML, Giuntini R, Greechie R (2004) Reasoning in quantum theory: sharp and unsharp quantum logic. Kluwer, Dordrecht"},{"key":"3157_CR8","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1017\/S1446788700036806","volume":"72","author":"A Dvure\u010denskij","year":"2001","unstructured":"Dvure\u010denskij A (2001) Pseudo MV algebras are intervals in \n                    \n                      \n                    \n                    $$\\ell $$\n                    \n                      \n                        \u2113\n                      \n                    \n                  -groups. J Aust Math Soc 72:427\u2013445","journal-title":"J Aust Math Soc"},{"key":"3157_CR9","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1016\/j.jal.2015.10.001","volume":"13","author":"A Dvure\u010denskij","year":"2015","unstructured":"Dvure\u010denskij A (2015) Lexicographic pseudo MV-algebras. J Appl Logic 13:825\u2013841","journal-title":"J Appl Logic"},{"key":"3157_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2422-7","volume-title":"New trends in quantum structures. Mathematics and its applications","author":"A Dvure\u010denskij","year":"2000","unstructured":"Dvure\u010denskij A, Pulmannov\u00e1 S (2000) New trends in quantum structures. Mathematics and its applications. Kluwer, Dordrecht"},{"key":"3157_CR11","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1023\/A:1004192715509","volume":"40","author":"A Dvure\u010denskij","year":"2001","unstructured":"Dvure\u010denskij A, Vetterlein T (2001a) Pseudoeffect algebras I, basic properties. Int J Theor Phys 40:685\u2013701","journal-title":"Int J Theor Phys"},{"key":"3157_CR12","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1023\/A:1004144832348","volume":"40","author":"A Dvure\u010denskij","year":"2001","unstructured":"Dvure\u010denskij A, Vetterlein T (2001b) Pseudoeffect algebras II, group representations. Int J Theor Phys 40:703\u2013726","journal-title":"Int J Theor Phys"},{"issue":"7\/8","key":"3157_CR13","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1023\/B:IJTP.0000048806.69906.11","volume":"43","author":"A Dvure\u010denskij","year":"2004","unstructured":"Dvure\u010denskij A, Vetterlein T (2004) Non-commutative algebras and quantum structures. Int J Theor Phys 43(7\/8):15\u201363","journal-title":"Int J Theor Phys"},{"key":"3157_CR14","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1007\/BF02283036","volume":"24","author":"DJ Foulis","year":"1994","unstructured":"Foulis DJ, Bennett MK (1994) Effect algebras and unsharp quantum logics. Found Phys 24:719\u2013742","journal-title":"Found Phys"},{"key":"3157_CR15","doi-asserted-by":"publisher","first-page":"2479","DOI":"10.1007\/s00500-011-0710-7","volume":"12","author":"DJ Foulis","year":"2011","unstructured":"Foulis DJ, Pulmannov\u00e1 S, Vincenkov\u00e1 E (2011) Lattice pseudoeffect algebras as double residuated structures. Soft Comput 12:2479\u20132488","journal-title":"Soft Comput"},{"key":"3157_CR16","first-page":"95","volume":"6","author":"G Georgescu","year":"2001","unstructured":"Georgescu G, Iorgulescu A (2001) Pseudo MV-algebras. Mult Valued Logic 6:95\u2013135","journal-title":"Mult Valued Logic"},{"key":"3157_CR17","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1007\/BF01889307","volume":"19","author":"R Giuntini","year":"1989","unstructured":"Giuntini R, Greuling H (1989) Toward a formal language for unsharp properties. Found Phys 19:931\u2013945","journal-title":"Found Phys"},{"key":"3157_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-9964-1","volume-title":"A guide to the literature on semirings and their applications in mathematics and information sciences","author":"K G\u0142azek","year":"2002","unstructured":"G\u0142azek K (2002) A guide to the literature on semirings and their applications in mathematics and information sciences. Springer, Berlin"},{"key":"3157_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jal.2016.04.001","volume":"16","author":"A Kadji","year":"2016","unstructured":"Kadji A, Lele C, Nganou JB (2016) A non-commutative generalization of \u0141ukasiewicz rings. J Appl Logic 16:1\u201313","journal-title":"J Appl Logic"},{"key":"3157_CR20","volume-title":"Orthomodular lattices, volume 18 of London mathematical society monographs","author":"G Kalmbach","year":"1983","unstructured":"Kalmbach G (1983) Orthomodular lattices, volume 18 of London mathematical society monographs. Academic Press, London"},{"key":"3157_CR21","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/0022-1236(86)90015-7","volume":"65","author":"D Mundici","year":"1986","unstructured":"Mundici D (1986) Interpretation of AFC\n                    \n                      \n                    \n                    $$^*$$\n                    \n                      \n                        \n                          \n                          \u2217\n                        \n                      \n                    \n                  -algebras in \u0141ukasiewicz sentential calculus. J Funct Anal 65:15\u201363","journal-title":"J Funct Anal"},{"key":"3157_CR22","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1023\/A:1021766309509","volume":"52","author":"J Rach\u016fnek","year":"2001","unstructured":"Rach\u016fnek J (2001) A non-commutative generalization of MV-algebras. Czechoslov Math J 52:255\u2013273","journal-title":"Czechoslov Math J"},{"issue":"6","key":"3157_CR23","first-page":"996","volume":"46","author":"P Vitolo","year":"2010","unstructured":"Vitolo P (2010) Compatibility and central elements in pseudo-effect algebras. Kybernetica 46(6):996\u20131008","journal-title":"Kybernetica"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-018-3157-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-018-3157-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-018-3157-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,24]],"date-time":"2019-03-24T00:57:33Z","timestamp":1553389053000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-018-3157-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,24]]},"references-count":23,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["3157"],"URL":"https:\/\/doi.org\/10.1007\/s00500-018-3157-2","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,24]]},"assertion":[{"value":"24 March 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declared that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}