{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T17:58:16Z","timestamp":1648922296092},"reference-count":36,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Algebra Appl."],"published-print":{"date-parts":[[2016,4]]},"abstract":"<jats:p> Yassemi\u2019s \u201csecond submodules\u201d are dualized and properties of its spectrum are studied. This is done by moving the ring theoretical setting to a lattice theoretical one and by introducing the notion of a (strongly) topological lattice [Formula: see text] with respect to a proper subset [Formula: see text] of [Formula: see text] We investigate and characterize (strongly) topological lattices in general in order to apply it to modules over associative unital rings. Given a non-zero left [Formula: see text]-module [Formula: see text] we introduce and investigate the spectrum [Formula: see text] of first submodules of [Formula: see text] as a dual notion of Yassemi\u2019s second submodules. We topologize [Formula: see text] and investigate the algebraic properties of [Formula: see text] by passing to the topological properties of the associated space. <\/jats:p>","DOI":"10.1142\/s0219498816500468","type":"journal-article","created":{"date-parts":[[2015,3,25]],"date-time":"2015-03-25T06:04:57Z","timestamp":1427263497000},"page":"1650046","source":"Crossref","is-referenced-by-count":3,"title":["On topological lattices and their applications to module theory"],"prefix":"10.1142","volume":"15","author":[{"given":"Jawad","family":"Abuhlail","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Box 5046, Dhahran, Kingdom of Saudi Arabia"}]},{"given":"Christian","family":"Lomp","sequence":"additional","affiliation":[{"name":"Centro de Matematica, Universidade do Porto, Rua Campo Alegre 687, 4169-007 Porto, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2016,1,27]]},"reference":[{"key":"S0219498816500468BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S1005386712000879"},{"key":"S0219498816500468BIB002","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2010.519748"},{"key":"S0219498816500468BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2010.11.021"},{"key":"S0219498816500468BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s10485-007-9088-1"},{"key":"S0219498816500468BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S1005386715000061"},{"issue":"6","key":"S0219498816500468BIB006","first-page":"23","volume":"9","author":"Abuhlail J. 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