{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:39:09Z","timestamp":1777703949818,"version":"3.51.4"},"reference-count":13,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2017,7,11]],"date-time":"2017-07-11T00:00:00Z","timestamp":1499731200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2017,7,21]]},"abstract":"<jats:p>\n                    This paper deals with strongly atomic algebraic lattices. Two necessary and sufficient conditions that a strongly atomic algebraic lattice is semimodular are shown by using the locally sublattice, called a\n                    <jats:italic>WAGC<\/jats:italic>\n                    sublattice, of the lattice.\n                  <\/jats:p>","DOI":"10.3233\/jifs-162168","type":"journal-article","created":{"date-parts":[[2017,7,11]],"date-time":"2017-07-11T11:22:36Z","timestamp":1499772156000},"page":"913-920","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Conditions that a strongly atomic algebraic lattice is semimodular"],"prefix":"10.1177","volume":"33","author":[{"given":"Peng","family":"He","sequence":"first","affiliation":[{"name":"College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xue-ping","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,7,11]]},"reference":[{"key":"e_1_3_1_2_2","first-page":"1","article-title":"Decomposition theory for lattices without chain conditions","volume":"97","author":"Crawley P.","year":"1960","unstructured":"CrawleyP. and DilworthR.P., Decomposition theory for lattices without chain conditions, Trans Amer Math Soc 97 (1960), 1\u201322.","journal-title":"Trans Amer Math Soc"},{"key":"e_1_3_1_3_2","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1090\/S0002-9947-1961-0120173-8","article-title":"Decomposition theory for non-semimodular lattices","volume":"99","author":"Crawley P.","year":"1961","unstructured":"CrawleyP., Decomposition theory for non-semimodular lattices, Trans Amer Math Soc 99 (1961), 246\u2013254 .","journal-title":"Trans Amer Math Soc"},{"key":"e_1_3_1_4_2","unstructured":"CrawleyP. and DilworthR.P. Algebraic theory of lattices Prentice Hall Englewood Cliffs NJ 1973."},{"key":"e_1_3_1_5_2","doi-asserted-by":"crossref","first-page":"2455","DOI":"10.1016\/j.aim.2010.05.001","article-title":"A cover-preserving embedding of semimodular lattices into geometric lattices","volume":"225","author":"Cz\u00e9dli G.","year":"2010","unstructured":"Cz\u00e9dliG. and Tam\u00e1s SchmidtE., A cover-preserving embedding of semimodular lattices into geometric lattices, Advances in Mathematics 225 (2010), 2455\u20132463.","journal-title":"Advances in Mathematics"},{"key":"e_1_3_1_6_2","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/0097-3165(92)90006-G","article-title":"Consistent dually semimodular lattices","volume":"60","author":"Gragg K.M.","year":"1992","unstructured":"GraggK.M. and KungJoseph P.S., Consistent dually semimodular lattices, Journal of Combinatorial Theory, Series A 60 (1992), 246\u2013263.","journal-title":"Journal of Combinatorial Theory, Series A"},{"key":"e_1_3_1_7_2","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/BF00367424","article-title":"A construction of semimodular lattices","volume":"2","author":"Gr\u00e4tzer G.","year":"1986","unstructured":"Gr\u00e4tzerG. and KissE.W., A construction of semimodular lattices, Order 2 (1986), 351\u2013365.","journal-title":"Order"},{"key":"e_1_3_1_8_2","doi-asserted-by":"crossref","unstructured":"Gr\u00e4tzerG. Lattice theory: Foundation Birkh\u00e4user Basel 2011.","DOI":"10.1007\/978-3-0348-0018-1"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1137\/0403022"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(93)90169-T"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(94)90213-5"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(02)00252-4"},{"key":"e_1_3_1_13_2","doi-asserted-by":"crossref","unstructured":"SchimmerlingE. A course on set theory Cambridge University Press 2011.","DOI":"10.1017\/CBO9780511996351"},{"key":"e_1_3_1_14_2","unstructured":"SternM. Semimordular lattice: Theory and applications Encyclopedia of Mathematics and its applications Cambridge University Press vol. 73 1999."}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-162168","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-162168","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-162168","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:40:03Z","timestamp":1777455603000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-162168"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,11]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,7,21]]}},"alternative-id":["10.3233\/JIFS-162168"],"URL":"https:\/\/doi.org\/10.3233\/jifs-162168","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,11]]}}}