{"id":"https://openalex.org/W2028695718","doi":"https://doi.org/10.1137/0214029","title":"On the Multiplicative Complexity of Modules over Associative Algebras","display_name":"On the Multiplicative Complexity of Modules over Associative Algebras","publication_year":1985,"publication_date":"1985-05-01","ids":{"openalex":"https://openalex.org/W2028695718","doi":"https://doi.org/10.1137/0214029","mag":"2028695718"},"language":"en","primary_location":{"id":"doi:10.1137/0214029","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214029","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008518666","display_name":"Werner Hartmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"W. Hartmann","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008518666"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5916,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.64196699,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"14","issue":"2","first_page":"383","last_page":"395"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.984000027179718,"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/T11476","display_name":"Graph theory and applications","score":0.984000027179718,"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":0.9761999845504761,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9577000141143799,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.7664405107498169},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7037924528121948},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.68741774559021},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6438982486724854},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5345228314399719},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5344125032424927},{"id":"https://openalex.org/keywords/associative-algebra","display_name":"Associative algebra","score":0.5031096339225769},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4933678209781647},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4404180347919464},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3344191908836365},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29708921909332275},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.2825220227241516},{"id":"https://openalex.org/keywords/division-algebra","display_name":"Division algebra","score":0.24788284301757812}],"concepts":[{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.7664405107498169},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7037924528121948},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.68741774559021},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6438982486724854},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5345228314399719},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5344125032424927},{"id":"https://openalex.org/C51292594","wikidata":"https://www.wikidata.org/wiki/Q744960","display_name":"Associative algebra","level":5,"score":0.5031096339225769},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4933678209781647},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4404180347919464},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3344191908836365},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29708921909332275},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.2825220227241516},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.24788284301757812},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0214029","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214029","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1968078911","https://openalex.org/W1993929164","https://openalex.org/W2088804960","https://openalex.org/W4234106236"],"related_works":["https://openalex.org/W2290501264","https://openalex.org/W1981095115","https://openalex.org/W2962919676","https://openalex.org/W1999987467","https://openalex.org/W4382322727","https://openalex.org/W2592509875","https://openalex.org/W3212738197","https://openalex.org/W73679669","https://openalex.org/W4293846289","https://openalex.org/W2950370295"],"abstract_inverted_index":{"The":[0],"complexity":[1],"$L(A,M)$":[2],"of":[3,17,20,28,31,37,59,63,69],"a":[4,9,67],"finite-dimensional":[5,10],"module":[6],"M":[7],"over":[8],"associative":[11],"algebra":[12,33],"A":[13,50],"is":[14,41,56],"the":[15,26,32,38,57],"number":[16,58],"nonscalar":[18],"multiplications/divisions":[19],"an":[21,29,35],"optimal":[22],"algorithm":[23],"to":[24,73],"compute":[25],"product":[27],"element":[30,36],"with":[34],"module.":[39],"It":[40],"known":[42],"that":[43],"\\[":[44],"L(A,A)":[45],"\\geqq":[46],"2":[47],"\\cdot":[48],"\\dim":[49],"-":[51],"s,":[52],"\\]":[53],"where":[54],"s":[55],"maximal":[60],"two-sided":[61],"ideals":[62],"A.":[64],"We":[65],"give":[66],"generalization":[68],"this":[70],"lower":[71],"bound":[72],"arbitrary":[74],"A-modules":[75],"M.":[76]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}