{"id":"https://openalex.org/W1758040183","doi":"https://doi.org/10.3968/j.ans.1715787020100302.033","title":"Reducible Property of a Finitely Generated Module","display_name":"Reducible Property of a Finitely Generated Module","publication_year":2010,"publication_date":"2010-08-18","ids":{"openalex":"https://openalex.org/W1758040183","doi":"https://doi.org/10.3968/j.ans.1715787020100302.033","mag":"1758040183"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.903.2699","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.903.2699","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cscanada.net/index.php/ans/article/download/j.ans.1715787020100302.033/963/","raw_type":"text"},"parent_works":[],"lineage":["https://openalex.org/W1758040183"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Lijiang Zeng","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lijiang Zeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4501,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.47818862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"3","issue":"2","first_page":"270","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.8871999979019165,"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"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.8871999979019165,"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/T10849","display_name":"Finite Group Theory Research","score":0.08060000091791153,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.011300000362098217,"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/completely-reducible-modules","display_name":"completely reducible modules","score":0.9769999980926514},{"id":"https://openalex.org/keywords/finitely-generated-modules","display_name":"finitely generated modules","score":0.9660000205039978},{"id":"https://openalex.org/keywords/group-rings","display_name":"group rings","score":0.8460000157356262}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.8916305899620056},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.7724736928939819},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6590986251831055},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5788882970809937},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5500147342681885},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.527618408203125},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.46537041664123535},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45186689496040344},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4460408389568329},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4143151044845581},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33496493101119995},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2643038034439087},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.903.2699","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.903.2699","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cscanada.net/index.php/ans/article/download/j.ans.1715787020100302.033/963/","raw_type":"text"},{"id":"mag:1758040183","doi":"https://doi.org/10.3968/j.ans.1715787020100302.033","is_oa":false,"landing_page_url":"http://www.cscanada.net/index.php/ans/article/download/j.ans.1715787020100302.033/963","pdf_url":null,"source":{"id":"https://openalex.org/S2764767664","display_name":"Advances in natural science/Advances in natural sciences","issn_l":"1715-7862","issn":["1715-7862"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Advances in natural science/Advances in natural sciences","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W598564470","https://openalex.org/W1543877612","https://openalex.org/W1675765252","https://openalex.org/W1968212654","https://openalex.org/W1993098007","https://openalex.org/W2061157583","https://openalex.org/W2164655498","https://openalex.org/W2225766620","https://openalex.org/W2385977541"],"related_works":["https://openalex.org/W2023707375","https://openalex.org/W4321327633","https://openalex.org/W4403632654","https://openalex.org/W6926693186","https://openalex.org/W2963315624","https://openalex.org/W2747255475","https://openalex.org/W4238272460","https://openalex.org/W4404922914","https://openalex.org/W4391364562"],"abstract_inverted_index":{"Abstract:":[0],"In":[1,168],"the":[2,75,104,144,169,179,203],"article,":[3],"G-invariant":[4],"element,":[5],"()HInv":[6],"V,":[7,67,94],"(":[8,133],",)RHom":[9],"U":[10],"V":[11,83,107,136,140],"and":[12,65,138],"other":[13],"concepts":[14],"were":[15,19],"introduced,":[16],"Several":[17],"lemmas":[18],"proved":[20,29],"to":[21,84],"use":[22],"these":[23],"concepts,":[24],"Finally,":[25],"it":[26,206],"had":[27],"been":[28],"that":[30,106,198,209],"let":[31,66],"F":[32],"be":[33,62,69,90,127,185,200],"a":[34,63,118,152,162,173],"field":[35],"whose":[36],"characteristic":[37],"dose":[38],"not":[39,220],"divide":[40],"|G|.":[41],"Then":[42],"every":[43],"finitely":[44,53,190],"generated":[45,54,191],"F[G]":[46],"module":[47,114,154,165],"is":[48,74,108,117,151,161,172,196,207],"completely":[49],"reducible.":[50],"Key":[51],"words:":[52],"R[G]":[55],"module;":[56],"B-projective;":[57],"R-homomorphism;":[58],"R-homomorphism":[59],"Let":[60,100,124],"A":[61,70,98,110,113,130,171,218],"ring":[64,174],"W":[68,95,137,142],"modules.":[71,99],"HomA(V,":[72],"W)":[73],"additive":[76],"abelian":[77],"group":[78],"of":[79,189],"all":[80,197],"homomorphisms":[81],"from":[82],"W,":[85],"The":[86],"same":[87],"notation":[88],"will":[89,184,199],"used":[91],"in":[92,181,187,202],"case":[93],"are":[96],"left":[97,112,163],"VA,":[101],"AV":[102],"denote":[103],"fact":[105],"an":[109],"module,":[111],"respectively.":[115],"V=AVB":[116],"two":[119],"sided":[120],"(A,":[121],"B)":[122],"module.":[123],"A,":[125],"B":[126,132,153,164],"rings,":[128],"Let,a":[129],"b":[131],",)Af":[134],"Hom":[135],"let,v":[139],"w":[141],"then":[143],"following":[145,170],"hold.":[146],"Lemma":[147,157],"1:":[148],"HomA(BVA,":[149],"WA)":[150],"with":[155,166],"(fb)v=f(bv).":[156],"2:":[158],"HomA(VA,":[159],"BWA)":[160],"(bf)v=b(fv).":[167],"which":[175],"satisfies":[176],"A.C.C":[177],"All":[178],"results":[180,211],"this":[182],"article":[183],"stated":[186],"terms":[188],"modules":[192,215],"(Jacobson,":[193],"1956).":[194],"This":[195],"required":[201],"sequel.":[204],"However":[205],"well-known":[208],"analogous":[210],"hold":[212],"for":[213],"arbitrary":[214],"even":[216],"if":[217],"does":[219],"satisfy":[221],"any":[222],"chain":[223],"condition.":[224]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2016-06-24T00:00:00"}
