{"id":"https://openalex.org/W2087068075","doi":"https://doi.org/10.1007/s00200-003-0138-0","title":"Principal Rings and their Invariant Factors","display_name":"Principal Rings and their Invariant Factors","publication_year":2003,"publication_date":"2003-11-01","ids":{"openalex":"https://openalex.org/W2087068075","doi":"https://doi.org/10.1007/s00200-003-0138-0","mag":"2087068075"},"language":"en","primary_location":{"id":"doi:10.1007/s00200-003-0138-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00200-003-0138-0","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000068391","display_name":"Jon A. Sjogren","orcid":null},"institutions":[{"id":"https://openalex.org/I4210099573","display_name":"United States Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93","country_code":"US","type":"government","lineage":["https://openalex.org/I1280414376","https://openalex.org/I1330347796","https://openalex.org/I4210099573","https://openalex.org/I4210102105","https://openalex.org/I4389425425"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jon A. Sjogren","raw_affiliation_strings":["Air Force Office of Scientific Research, 4015 Wilson Blvd., Ballston Station, VA, 22203, USA","Air Force Office of Scientific Research"],"affiliations":[{"raw_affiliation_string":"Air Force Office of Scientific Research, 4015 Wilson Blvd., Ballston Station, VA, 22203, USA","institution_ids":["https://openalex.org/I4210099573"]},{"raw_affiliation_string":"Air Force Office of Scientific Research","institution_ids":["https://openalex.org/I4210099573"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000068391"],"corresponding_institution_ids":["https://openalex.org/I4210099573"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.5785,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64720812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"4","first_page":"287","last_page":"328"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9972000122070312,"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":0.9972000122070312,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9804999828338623,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9771999716758728,"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/mathematics","display_name":"Mathematics","score":0.7143268585205078},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.5891338586807251},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5550798177719116},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5490215420722961},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.49052757024765015},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.45351946353912354},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.4396926164627075},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4359610974788666},{"id":"https://openalex.org/keywords/ring-theory","display_name":"Ring theory","score":0.4286549389362335},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.41835272312164307},{"id":"https://openalex.org/keywords/semiprime-ring","display_name":"Semiprime ring","score":0.41684114933013916},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.384891152381897},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.17628085613250732},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16680550575256348},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10175645351409912}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7143268585205078},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.5891338586807251},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5550798177719116},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5490215420722961},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.49052757024765015},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.45351946353912354},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.4396926164627075},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4359610974788666},{"id":"https://openalex.org/C196434610","wikidata":"https://www.wikidata.org/wiki/Q1208658","display_name":"Ring theory","level":4,"score":0.4286549389362335},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.41835272312164307},{"id":"https://openalex.org/C177598507","wikidata":"https://www.wikidata.org/wiki/Q2269249","display_name":"Semiprime ring","level":3,"score":0.41684114933013916},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.384891152381897},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.17628085613250732},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16680550575256348},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10175645351409912},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00200-003-0138-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00200-003-0138-0","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W10008895","https://openalex.org/W569064703","https://openalex.org/W586848920","https://openalex.org/W629265671","https://openalex.org/W631562622","https://openalex.org/W1588205362","https://openalex.org/W1599097467","https://openalex.org/W1879453234","https://openalex.org/W1973673887","https://openalex.org/W2024874060","https://openalex.org/W2044540217","https://openalex.org/W2049707341","https://openalex.org/W2065842485","https://openalex.org/W2067136705","https://openalex.org/W2073761272","https://openalex.org/W2094831196","https://openalex.org/W2798813531"],"related_works":["https://openalex.org/W2352074369","https://openalex.org/W3142685117","https://openalex.org/W2176261248","https://openalex.org/W2594491092","https://openalex.org/W4308298797","https://openalex.org/W2040720675","https://openalex.org/W2977639652","https://openalex.org/W4302010613","https://openalex.org/W2039990202","https://openalex.org/W1905329293"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}