{"id":"https://openalex.org/W1245804045","doi":"https://doi.org/10.2478/forma-2014-0029","title":"The First Isomorphism Theorem and Other Properties of Rings","display_name":"The First Isomorphism Theorem and Other Properties of Rings","publication_year":2014,"publication_date":"2014-12-01","ids":{"openalex":"https://openalex.org/W1245804045","doi":"https://doi.org/10.2478/forma-2014-0029","mag":"1245804045"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2014-0029","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2014-0029","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2014-0029","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/forma-2014-0029","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090121372","display_name":"Artur Korni\u0142owicz","orcid":"https://orcid.org/0000-0002-4565-9082"},"institutions":[{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Artur Korni\u0142owicz","raw_affiliation_strings":["Institute of Informatics University of Bia\u0142ystok Sosnowa 64, 15-887 Bia\u0142ystok Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics University of Bia\u0142ystok Sosnowa 64, 15-887 Bia\u0142ystok Poland","institution_ids":["https://openalex.org/I245364917"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048465549","display_name":"Christoph Schwarzweller","orcid":"https://orcid.org/0000-0001-9587-8737"},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]},{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Christoph Schwarzweller","raw_affiliation_strings":["Institute of Computer Science University of Gdansk Wita Stwosza 57, 80-952 Gdansk Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science University of Gdansk Wita Stwosza 57, 80-952 Gdansk Poland","institution_ids":["https://openalex.org/I40413290","https://openalex.org/I4210087266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.168,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.71803473,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"22","issue":"4","first_page":"291","last_page":"301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9980999827384949,"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":0.9980999827384949,"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":0.9649999737739563,"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":0.9239000082015991,"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":0.8925106525421143},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.7303563356399536},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.6386054754257202},{"id":"https://openalex.org/keywords/isomorphism-theorem","display_name":"Isomorphism theorem","score":0.6342110633850098},{"id":"https://openalex.org/keywords/principal-ideal","display_name":"Principal ideal","score":0.5752723217010498},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5648927688598633},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.5123699903488159},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.48033395409584045},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4757499396800995},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.4617026448249817},{"id":"https://openalex.org/keywords/factorial","display_name":"Factorial","score":0.441012978553772},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.42829716205596924},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3869577646255493},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3685058057308197},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3675832748413086}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8925106525421143},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.7303563356399536},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.6386054754257202},{"id":"https://openalex.org/C26231708","wikidata":"https://www.wikidata.org/wiki/Q1065966","display_name":"Isomorphism theorem","level":2,"score":0.6342110633850098},{"id":"https://openalex.org/C78766492","wikidata":"https://www.wikidata.org/wiki/Q44382","display_name":"Principal ideal","level":3,"score":0.5752723217010498},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5648927688598633},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.5123699903488159},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.48033395409584045},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4757499396800995},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.4617026448249817},{"id":"https://openalex.org/C183763347","wikidata":"https://www.wikidata.org/wiki/Q120976","display_name":"Factorial","level":2,"score":0.441012978553772},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.42829716205596924},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3869577646255493},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3685058057308197},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3675832748413086},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/forma-2014-0029","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2014-0029","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2014-0029","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:214c7a56432c4f65a87b4f2ecc56f3ff","is_oa":false,"landing_page_url":"https://doaj.org/article/214c7a56432c4f65a87b4f2ecc56f3ff","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 22, Iss 4, Pp 291-301 (2014)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/3725","is_oa":false,"landing_page_url":"http://hdl.handle.net/11320/3725","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/forma-2014-0029","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2014-0029","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2014-0029","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1245804045.pdf","grobid_xml":"https://content.openalex.org/works/W1245804045.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W22141270","https://openalex.org/W180239714","https://openalex.org/W192809544","https://openalex.org/W260340778","https://openalex.org/W1041138052","https://openalex.org/W1596666806","https://openalex.org/W2027056083","https://openalex.org/W2027654459","https://openalex.org/W2069069851","https://openalex.org/W2096867974","https://openalex.org/W2098464720","https://openalex.org/W2105559527","https://openalex.org/W2115474581","https://openalex.org/W2138253682","https://openalex.org/W2140950626","https://openalex.org/W2143224343","https://openalex.org/W2143851127","https://openalex.org/W2147599721","https://openalex.org/W2150348213","https://openalex.org/W2159772409","https://openalex.org/W2163090560","https://openalex.org/W2163641194","https://openalex.org/W2165871412","https://openalex.org/W2296232473","https://openalex.org/W2304533832","https://openalex.org/W2330022088","https://openalex.org/W2335917076","https://openalex.org/W2338095303","https://openalex.org/W2547540153","https://openalex.org/W2912565176","https://openalex.org/W3183392806","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3143269295","https://openalex.org/W4312973762","https://openalex.org/W2056695797","https://openalex.org/W2389993406","https://openalex.org/W2984338298","https://openalex.org/W1973611015","https://openalex.org/W2373858638","https://openalex.org/W2354689617","https://openalex.org/W2139654767","https://openalex.org/W2075381343"],"abstract_inverted_index":{"Summary":[0],"Different":[1],"properties":[2],"of":[3],"rings":[4,63],"and":[5,11,19,21,46,49,68],"fields":[6,65],"are":[7,66],"discussed":[8],"[12],":[9],"[41]":[10],"[17].":[12],"We":[13],"introduce":[14],"ring":[15],"homomorphisms,":[16],"their":[17],"kernels":[18],"images,":[20],"prove":[22],"the":[23],"First":[24],"Isomorphism":[25],"Theorem,":[26],"namely":[27],"that":[28,51,61],"for":[29],"a":[30],"homomorphism":[31],"f":[32],":":[33],"R":[34],"\u2192":[35],"S":[36],"we":[37,43,59],"have":[38],"R/ker(f)":[39],"\u2245":[40],"Im(f).":[41],"Then":[42],"define":[44],"prime":[45],"irreducible":[47],"elements":[48],"show":[50,60],"every":[52],"principal":[53],"ideal":[54],"domain":[55],"is":[56],"factorial.":[57],"Finally":[58],"polynomial":[62],"over":[64],"Euclidean":[67],"hence":[69],"also":[70],"factorial":[71]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
