{"id":"https://openalex.org/W7203544201","doi":"https://doi.org/10.63689/2993-7159.1354","title":"Foundations of Neutrosophic N-Semirings Theory and Structural Properties","display_name":"Foundations of Neutrosophic N-Semirings Theory and Structural Properties","publication_year":2026,"publication_date":"2026-07-31","ids":{"openalex":"https://openalex.org/W7203544201","doi":"https://doi.org/10.63689/2993-7159.1354"},"language":"en","primary_location":{"id":"doi:10.63689/2993-7159.1354","doi":"https://doi.org/10.63689/2993-7159.1354","is_oa":true,"landing_page_url":"https://doi.org/10.63689/2993-7159.1354","pdf_url":null,"source":{"id":"https://openalex.org/S4387292478","display_name":"Neutrosophic Systems with Applications","issn_l":"2993-7140","issn":["2993-7140","2993-7159"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310316495","host_organization_name":"University of New Mexico Press","host_organization_lineage":["https://openalex.org/P4310316495"],"host_organization_lineage_names":["University of New Mexico Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neutrosophic Systems with Applications","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W7203544201"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.63689/2993-7159.1354","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005241217","display_name":"Raja Muhammad Hashim","orcid":"https://orcid.org/0009-0003-9983-2842","observed_orcids":["https://orcid.org/0009-0003-9983-2842"]},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Raja Muhammad Hashim","raw_affiliation_strings":["Department of Mathematics and Statistics, Faculty of Natural and Computational Science, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Faculty of Natural and Computational Science, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030602859","display_name":"Muhammad Gulistan","orcid":"https://orcid.org/0000-0002-0314-876X","observed_orcids":["https://orcid.org/0000-0002-0314-876X"]},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Gulistan","raw_affiliation_strings":["Department of Mathematics and Statistics, Faculty of Natural and Computational Science, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Faculty of Natural and Computational Science, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5135987159","display_name":"Muhammad Shahzad","orcid":"https://orcid.org/0009-0002-9394-343X","observed_orcids":["https://orcid.org/0009-0002-9394-343X"]},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Shahzad","raw_affiliation_strings":["Department of Mathematics and Statistics, Faculty of Natural and Computational Science, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Faculty of Natural and Computational Science, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I263208278"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I263208278"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"7","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.5238999724388123,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.5238999724388123,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.41280001401901245,"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"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.023900000378489494,"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/substructure","display_name":"substructure","score":0.7630000114440918},{"id":"https://openalex.org/keywords/left-ideals","display_name":"left ideals","score":0.8009999990463257},{"id":"https://openalex.org/keywords/right-ideals","display_name":"right ideals","score":1.0},{"id":"https://openalex.org/keywords/two-sided-ideals","display_name":"two-sided ideals","score":0.9779999852180481},{"id":"https://openalex.org/keywords/congruence-relations","display_name":"congruence relations","score":0.949999988079071},{"id":"https://openalex.org/keywords/algebraic-structures","display_name":"algebraic structures","score":0.8579999804496765}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4345000088214874},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3192000091075897},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2451000064611435},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.24449999630451202},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.24070000648498535},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.23839999735355377},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.23680000007152557}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.63689/2993-7159.1354","doi":"https://doi.org/10.63689/2993-7159.1354","is_oa":true,"landing_page_url":"https://doi.org/10.63689/2993-7159.1354","pdf_url":null,"source":{"id":"https://openalex.org/S4387292478","display_name":"Neutrosophic Systems with Applications","issn_l":"2993-7140","issn":["2993-7140","2993-7159"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310316495","host_organization_name":"University of New Mexico Press","host_organization_lineage":["https://openalex.org/P4310316495"],"host_organization_lineage_names":["University of New Mexico Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neutrosophic Systems with Applications","raw_type":"journal-article"},{"id":"pmh:oai:digitalrepository.unm.edu:nss_journal-4052","doi":null,"is_oa":true,"landing_page_url":"https://digitalrepository.unm.edu/nss_journal/vol100/iss1/10","pdf_url":"https://digitalrepository.unm.edu/context/nss_journal/article/4052/viewcontent/10FoundationsNeutrosophic.pdf","source":{"id":"https://openalex.org/S4377196368","display_name":"UNM\u2019s Digital Repository (University of New Mexico)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I169521973","host_organization_name":"University of New Mexico","host_organization_lineage":["https://openalex.org/I169521973"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Neutrosophic Sets and Systems","raw_type":"text"},{"id":"doi:10.5281/zenodo.21957521","doi":"https://doi.org/10.5281/zenodo.21957521","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21957521","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"JournalArticle"},{"id":"doi:10.5281/zenodo.21957522","doi":"https://doi.org/10.5281/zenodo.21957522","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21957522","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"doi:10.63689/2993-7159.1354","doi":"https://doi.org/10.63689/2993-7159.1354","is_oa":true,"landing_page_url":"https://doi.org/10.63689/2993-7159.1354","pdf_url":null,"source":{"id":"https://openalex.org/S4387292478","display_name":"Neutrosophic Systems with Applications","issn_l":"2993-7140","issn":["2993-7140","2993-7159"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310316495","host_organization_name":"University of New Mexico Press","host_organization_lineage":["https://openalex.org/P4310316495"],"host_organization_lineage_names":["University of New Mexico Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neutrosophic Systems with Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203544201.pdf","grobid_xml":"https://content.openalex.org/works/W7203544201.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4226143358","https://openalex.org/W4408471518","https://openalex.org/W225281798","https://openalex.org/W2149357117","https://openalex.org/W3048611994","https://openalex.org/W2793531440","https://openalex.org/W4411520577","https://openalex.org/W4200404317","https://openalex.org/W3210106346","https://openalex.org/W4388679254"],"abstract_inverted_index":{"In":[0],"this":[1,116],"paper":[2],"the":[3,54,88,109],"concept":[4],"of":[5,25,72,111],"neutrosophic":[6,73],"n-semirings":[7,26,74],"(S\u222a":[8,27],"I,":[9,28],"\u2217":[10,12,14,16,18,29,31,33,35,37],"1,":[11,30],"2,":[13,32],"3,...,":[15,34],"n,":[17,36],"n+1)":[19,38],"has":[20,39],"been":[21,40,47,63,76,99],"introduced.":[22],"The":[23,65],"substructure":[24],"defined":[41],"and":[42,68,90,93],"some":[43,59,94],"useful":[44],"results":[45],"have":[46,62,75,83,97,104],"proved.":[48],"Moreover,":[49],"in":[50,115],"order":[51],"to":[52,107],"familiarize":[53],"readers":[55],"with":[56],"these":[57],"concepts":[58],"worthy":[60],"examples":[61,106],"coined.":[64],"left,":[66],"right":[67],"two":[69],"sided":[70],"ideals":[71],"paid":[77],"a":[78],"special":[79],"heed.":[80],"Finally":[81],"we":[82,102],"turned":[84],"our":[85],"discussion":[86],"towards":[87],"compatible":[89],"congruence":[91],"relations":[92],"remarkable":[95],"properties":[96],"also":[98],"considered.":[100],"Furthermore,":[101],"vividly":[103],"given":[105],"express":[108],"rationality":[110],"each":[112],"notion":[113],"popularized":[114],"paper.":[117]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-08-16T00:00:00"}
