{"id":"https://openalex.org/W4417124738","doi":"https://doi.org/10.3390/axioms14120876","title":"Additive Derivations of Incidence Modules","display_name":"Additive Derivations of Incidence Modules","publication_year":2025,"publication_date":"2025-11-28","ids":{"openalex":"https://openalex.org/W4417124738","doi":"https://doi.org/10.3390/axioms14120876"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14120876","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14120876","pdf_url":"https://www.mdpi.com/2075-1680/14/12/876/pdf","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/12/876/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Naseer Ullah","orcid":"https://orcid.org/0009-0008-4586-8950"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Naseer Ullah","raw_affiliation_strings":["School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China"],"raw_orcid":"https://orcid.org/0009-0008-4586-8950","affiliations":[{"raw_affiliation_string":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101930614","display_name":"Hailou Yao","orcid":"https://orcid.org/0000-0002-0876-8765"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hailou Yao","raw_affiliation_strings":["School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107615233","display_name":"Dalal Alhwikem","orcid":null},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Dalal Alhwikem","raw_affiliation_strings":["Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5092253445","display_name":"Imran Shabir Chuhan","orcid":"https://orcid.org/0000-0002-3125-8245"},"institutions":[{"id":"https://openalex.org/I178777954","display_name":"Kohat University of Science and Technology","ror":"https://ror.org/057d2v504","country_code":"PK","type":"education","lineage":["https://openalex.org/I178777954"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Imran Shabir Chuhan","raw_affiliation_strings":["Department of Mathematics, University of Kotli AJK, Kotli 11100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kotli AJK, Kotli 11100, Pakistan","institution_ids":["https://openalex.org/I178777954"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I37796252"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.43388849,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"12","first_page":"876","last_page":"876"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.39980000257492065,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.39980000257492065,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.29670000076293945,"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":0.09239999949932098,"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":0.6407999992370605},{"id":"https://openalex.org/keywords/incidence","display_name":"Incidence (geometry)","score":0.59170001745224},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5799000263214111},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5181000232696533},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4747999906539917},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.4706000089645386},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4697999954223633},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.4318999946117401}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8149999976158142},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.6407999992370605},{"id":"https://openalex.org/C61511704","wikidata":"https://www.wikidata.org/wiki/Q1671857","display_name":"Incidence (geometry)","level":2,"score":0.59170001745224},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5799000263214111},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5181000232696533},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4860999882221222},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4747999906539917},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.4706000089645386},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4697999954223633},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.4318999946117401},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.41280001401901245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3953000009059906},{"id":"https://openalex.org/C115179944","wikidata":"https://www.wikidata.org/wiki/Q371133","display_name":"Incidence algebra","level":5,"score":0.3905999958515167},{"id":"https://openalex.org/C2989065042","wikidata":"https://www.wikidata.org/wiki/Q7378971","display_name":"Algebraic properties","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33230000734329224},{"id":"https://openalex.org/C35729967","wikidata":"https://www.wikidata.org/wiki/Q18848","display_name":"Module","level":4,"score":0.30889999866485596},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.2937999963760376},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C142109727","wikidata":"https://www.wikidata.org/wiki/Q1142704","display_name":"Local ring","level":3,"score":0.26989999413490295},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14120876","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14120876","pdf_url":"https://www.mdpi.com/2075-1680/14/12/876/pdf","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:279e7844e903481fbe40fe199fe7c9ec","is_oa":true,"landing_page_url":"https://doaj.org/article/279e7844e903481fbe40fe199fe7c9ec","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":"Axioms, Vol 14, Iss 12, p 876 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14120876","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14120876","pdf_url":"https://www.mdpi.com/2075-1680/14/12/876/pdf","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2186466424","display_name":null,"funder_award_id":"QU-APC-2025","funder_id":"https://openalex.org/F4320324403","funder_display_name":"Qassim University"}],"funders":[{"id":"https://openalex.org/F4320324403","display_name":"Qassim University","ror":"https://ror.org/01wsfe280"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4417124738.pdf","grobid_xml":"https://content.openalex.org/works/W4417124738.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1992126512","https://openalex.org/W2029236081","https://openalex.org/W2071328237","https://openalex.org/W2075500376","https://openalex.org/W2161396108","https://openalex.org/W2962746733","https://openalex.org/W2963074707","https://openalex.org/W2963288699","https://openalex.org/W4237496336","https://openalex.org/W4240899876"],"related_works":[],"abstract_inverted_index":{"Let":[0],"R":[1,30],"be":[2],"an":[3,44],"associative":[4],"ring":[5,29],"and":[6,31,59,81],"M":[7,26],"a":[8,24,28,32,39,57,71,88],"left":[9],"R-module.":[10],"This":[11],"paper":[12],"examines":[13],"the":[14,18,52,75,79,82],"structural":[15],"properties":[16,77],"of":[17,42,78,85],"incidence":[19],"module":[20,25,80],"I(P,M),":[21],"associated":[22],"with":[23],"over":[27],"locally":[33],"finite":[34,58],"poset":[35],"P.":[36],"We":[37],"provide":[38],"complete":[40],"characterization":[41],"when":[43],"additive":[45],"derivation":[46],"on":[47],"I(P,M)":[48],"is":[49,56],"inner,":[50],"for":[51],"case":[53],"where":[54],"P":[55,86],"connected":[60],"poset.":[61],"These":[62],"criteria":[63],"are":[64],"then":[65],"generalized":[66],"to":[67],"arbitrary":[68],"posets,":[69],"revealing":[70],"profound":[72],"connection":[73],"between":[74],"algebraic":[76],"graph-theoretic":[83],"structure":[84],"as":[87],"directed":[89],"graph.":[90]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-12-08T00:00:00"}
