{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T10:10:15Z","timestamp":1726222215566},"reference-count":7,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T00:00:00Z","timestamp":1686700800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T00:00:00Z","timestamp":1686700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Order"],"published-print":{"date-parts":[[2024,8]]},"DOI":"10.1007\/s11083-023-09640-y","type":"journal-article","created":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T07:02:12Z","timestamp":1686726132000},"page":"471-483","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Dedekind-MacNeille Completion of a Poset as a Set of Ideals of the Incidence Algebra"],"prefix":"10.1007","volume":"41","author":[{"given":"Manfred","family":"Dugas","sequence":"first","affiliation":[]},{"given":"Daniel","family":"Herden","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,14]]},"reference":[{"key":"9640_CR1","doi-asserted-by":"crossref","unstructured":"Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press (2002)","DOI":"10.1017\/CBO9780511809088"},{"key":"9640_CR2","doi-asserted-by":"publisher","first-page":"106336","DOI":"10.1016\/j.jpaa.2020.106336","volume":"224","author":"M Dugas","year":"2020","unstructured":"Dugas, M., Herden, D., Rebrovich, J.: Indecomposable ideals of finitary incidence algebras. J. Pure Appl. Algebra 224, 106336 (2020)","journal-title":"J. Pure Appl. Algebra"},{"key":"9640_CR3","first-page":"30","volume":"34","author":"NS Khripchenko","year":"2010","unstructured":"Khripchenko, N.S.: Finitary incidence algebras of quasiorders. Mat. Stud. 34, 30\u201337 (2010)","journal-title":"Mat. Stud."},{"key":"9640_CR4","doi-asserted-by":"publisher","first-page":"1670","DOI":"10.1080\/00927870802210019","volume":"37","author":"NS Khripchenko","year":"2009","unstructured":"Khripchenko, N.S., Novikov, B.V.: Finitary incidence algebras. Comm. Algebra 37, 1670\u20131676 (2009)","journal-title":"Comm. Algebra"},{"key":"9640_CR5","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1007\/BF00531932","volume":"2","author":"G-C Rota","year":"1964","unstructured":"Rota, G.-C.: On the foundations of combinatorial theory I: theory of M\u00f6bius functions. Z. Wahrscheinlichkeitstheorie 2, 340\u2013368 (1964)","journal-title":"Z. Wahrscheinlichkeitstheorie"},{"key":"9640_CR6","unstructured":"Spiegel, E., O\u2019Donnell, C.J.: Incidence Algebras, Monogr. Textbooks Pure Appl. Math. 206, Marcel Dekker (1997)"},{"key":"9640_CR7","doi-asserted-by":"publisher","first-page":"2491","DOI":"10.1142\/S0217732303012738","volume":"18","author":"RD Sorkin","year":"2003","unstructured":"Sorkin, R.D.: Indecomposable ideals in incidence algebras. Modern Phys. Lett. A 18, 2491\u20132499 (2003)","journal-title":"Modern Phys. Lett. A"}],"container-title":["Order"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-023-09640-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11083-023-09640-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-023-09640-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T09:11:34Z","timestamp":1726218694000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11083-023-09640-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,14]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["9640"],"URL":"https:\/\/doi.org\/10.1007\/s11083-023-09640-y","relation":{},"ISSN":["0167-8094","1572-9273"],"issn-type":[{"type":"print","value":"0167-8094"},{"type":"electronic","value":"1572-9273"}],"subject":[],"published":{"date-parts":[[2023,6,14]]},"assertion":[{"value":"4 October 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 May 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 June 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}