{"id":"https://openalex.org/W2142614293","doi":"https://doi.org/10.1007/s10998-014-0029-0","title":"The M-principal graph of a commutative ring","display_name":"The M-principal graph of a commutative ring","publication_year":2014,"publication_date":"2014-05-26","ids":{"openalex":"https://openalex.org/W2142614293","doi":"https://doi.org/10.1007/s10998-014-0029-0","mag":"2142614293"},"language":"en","primary_location":{"id":"doi:10.1007/s10998-014-0029-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10998-014-0029-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10998-014-0029-0.pdf","source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10998-014-0029-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033659538","display_name":"M. J. Nikmehr","orcid":null},"institutions":[{"id":"https://openalex.org/I80543232","display_name":"K.N.Toosi University of Technology","ror":"https://ror.org/0433abe34","country_code":"IR","type":"education","lineage":["https://openalex.org/I80543232"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"M. J. Nikmehr","raw_affiliation_strings":["Faculty of Mathematics, K.N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran","K.N. Toosi university of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, K.N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran","institution_ids":["https://openalex.org/I80543232"]},{"raw_affiliation_string":"K.N. Toosi university of Technology","institution_ids":["https://openalex.org/I80543232"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001007399","display_name":"F. Heydari","orcid":"https://orcid.org/0000-0002-8944-4729"},"institutions":[{"id":"https://openalex.org/I110525433","display_name":"Islamic Azad University, Tehran","ror":"https://ror.org/01kzn7k21","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433"]},{"id":"https://openalex.org/I204588832","display_name":"Islamic Azad University, Karaj","ror":"https://ror.org/01y4xm534","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I204588832"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"F. Heydari","raw_affiliation_strings":["Department of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad University, Alborz, Iran","Islamic Azad, University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad University, Alborz, Iran","institution_ids":["https://openalex.org/I204588832"]},{"raw_affiliation_string":"Islamic Azad, University","institution_ids":["https://openalex.org/I110525433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5033659538"],"corresponding_institution_ids":["https://openalex.org/I80543232"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":2.7562,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.90282876,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"68","issue":"2","first_page":"185","last_page":"192"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9998000264167786,"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":0.9998000264167786,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9968000054359436,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9887999892234802,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8867437839508057},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.7248242497444153},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.693874180316925},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6728307008743286},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6338428258895874},{"id":"https://openalex.org/keywords/backslash","display_name":"Backslash","score":0.5819690823554993},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.43744373321533203},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3859257698059082}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8867437839508057},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.7248242497444153},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.693874180316925},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6728307008743286},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6338428258895874},{"id":"https://openalex.org/C2780345915","wikidata":"https://www.wikidata.org/wiki/Q11185","display_name":"Backslash","level":2,"score":0.5819690823554993},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.43744373321533203},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3859257698059082}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10998-014-0029-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10998-014-0029-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10998-014-0029-0.pdf","source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10998-014-0029-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10998-014-0029-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10998-014-0029-0.pdf","source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2142614293.pdf","grobid_xml":"https://content.openalex.org/works/W2142614293.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W331738969","https://openalex.org/W1495550473","https://openalex.org/W1548944036","https://openalex.org/W1987843142","https://openalex.org/W2014392116","https://openalex.org/W2038638518","https://openalex.org/W2045052586","https://openalex.org/W2049707341","https://openalex.org/W2073343653","https://openalex.org/W2078196686","https://openalex.org/W4230659398","https://openalex.org/W4292806204","https://openalex.org/W4296292757"],"related_works":["https://openalex.org/W1885115167","https://openalex.org/W4308298797","https://openalex.org/W4255963200","https://openalex.org/W2360590989","https://openalex.org/W4255391830","https://openalex.org/W2369074270","https://openalex.org/W2408222820","https://openalex.org/W2741158649","https://openalex.org/W2253391970","https://openalex.org/W2949282300"],"abstract_inverted_index":{"Let":[0],"$$R$$":[1,10,22],"be":[2,8],"a":[3],"commutative":[4],"ring":[5],"and":[6,39,44,49,69,83],"$$M$$":[7,18],"an":[9],"-module.":[11],"In":[12,54],"this":[13],"paper,":[14],"we":[15],"introduce":[16],"the":[17,30,55],"-principal":[19],"graph":[20,31],"of":[21,72],",":[23,38],"denoted":[24,62],"by":[25,63],"$$M-PG(R)$$":[26,84],".":[27,53,65],"It":[28],"is":[29,35,61],"whose":[32],"vertex":[33],"set":[34],"$$R\\backslash":[36],"\\{0\\}$$":[37],"two":[40,74],"distinct":[41],"vertices":[42],"$$x$$":[43],"$$y$$":[45],"are":[46,76,85],"adjacent":[47],"if":[48,51],"only":[50],"$$xM=yM$$":[52],"special":[56],"case":[57],"that":[58],"$$M=R,":[59],"M-PG(R)$$":[60],"$$PG(R)$$":[64,82],"The":[66],"basic":[67],"properties":[68],"possible":[70],"structures":[71],"these":[73],"graphs":[75],"studied.":[77],"Also,":[78],"some":[79],"relations":[80],"between":[81],"established.":[86]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}