{"id":"https://openalex.org/W1979265906","doi":"https://doi.org/10.1155/2011/920737","title":"Topological Aspects of the Product of Lattices","display_name":"Topological Aspects of the Product of Lattices","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1979265906","doi":"https://doi.org/10.1155/2011/920737","mag":"1979265906"},"language":"en","primary_location":{"id":"doi:10.1155/2011/920737","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/920737","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/920737.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2011/920737.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058901485","display_name":"Carmen Vlad","orcid":null},"institutions":[{"id":"https://openalex.org/I126863827","display_name":"Pace University","ror":"https://ror.org/047p7y759","country_code":"US","type":"education","lineage":["https://openalex.org/I126863827"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Carmen Vlad","raw_affiliation_strings":["Department of Mathematics, Pace University, Pleasantville, NY 10570, USA pace.edu","(Pace University)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pace University, Pleasantville, NY 10570, USA pace.edu","institution_ids":["https://openalex.org/I126863827"]},{"raw_affiliation_string":"(Pace University)","institution_ids":["https://openalex.org/I126863827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058901485"],"corresponding_institution_ids":["https://openalex.org/I126863827"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06938094,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2011","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9048526287078857},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.6801259517669678},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5830999612808228},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.5587723255157471},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5421321392059326},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46527644991874695},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42732998728752136},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42287421226501465},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.410074383020401},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3614347577095032},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3560396730899811},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.335185706615448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9048526287078857},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.6801259517669678},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5830999612808228},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.5587723255157471},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5421321392059326},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46527644991874695},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42732998728752136},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42287421226501465},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.410074383020401},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3614347577095032},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3560396730899811},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.335185706615448},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2011/920737","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/920737","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/920737.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:920737","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2011/920737.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:acfd93a2068b423daa8f03255dcb5ea3","is_oa":true,"landing_page_url":"https://doaj.org/article/acfd93a2068b423daa8f03255dcb5ea3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2011 (2011)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2011/920737","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/920737","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/920737.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1979265906.pdf","grobid_xml":"https://content.openalex.org/works/W1979265906.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2085826626","https://openalex.org/W2169986191","https://openalex.org/W2397756605","https://openalex.org/W2500124111"],"related_works":["https://openalex.org/W2032233321","https://openalex.org/W3121970507","https://openalex.org/W2110028391","https://openalex.org/W54497855","https://openalex.org/W217960748","https://openalex.org/W3125814499","https://openalex.org/W2090827041","https://openalex.org/W2565703248","https://openalex.org/W187246281","https://openalex.org/W2143548620"],"abstract_inverted_index":{"Let":[0],"X":[1,14,19],"be":[2],"an":[3],"arbitrary":[4],"nonempty":[5],"set":[6],"and":[7,34,86],"L":[8,21,25,32,37,49,55,63],"a":[9,89],"lattice":[10],"of":[11,13,60,67,78,80,88,91],"subsets":[12],"such":[15],"that":[16],"\u2205":[17],",":[18,33],"\u2208":[20],".":[22],"A":[23,47],"(":[24,36,48,54,62],")":[26,38,56,64],"denotes":[27,39,57],"the":[28,58,68],"algebra":[29],"generated":[30],"by":[31],"M":[35,61],"those":[40],"nonnegative,":[41],"finite,":[42],"finitely":[43],"additive":[44],"measures":[45],"on":[46],").":[50],"In":[51],"addition,":[52],"I":[53],"subset":[59],"which":[65],"consists":[66],"nontrivial":[69],"zero\u2010one":[70],"valued":[71],"measures.":[72,92],"The":[73],"paper":[74],"gives":[75],"detailed":[76],"analysis":[77],"products":[79,87],"lattices,":[81],"their":[82],"associated":[83],"Wallman":[84],"spaces,":[85],"variety":[90]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
