{"id":"https://openalex.org/W2576462951","doi":null,"title":"Decomposition of Rings under the Circle Operation","display_name":"Decomposition of Rings under the Circle Operation","publication_year":null,"publication_date":null,"ids":{"openalex":"https://openalex.org/W2576462951","mag":"2576462951"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.94.7047","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.94.7047","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/BAG/vol.43/no.1/b43h1eas.pdf","raw_type":"text"},"parent_works":[],"lineage":["https://openalex.org/W2576462951"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":[],"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/A5075580982","display_name":"Clare Coleman","orcid":"https://orcid.org/0000-0002-6151-3390","observed_orcids":["https://orcid.org/0000-0002-6151-3390"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Clare Coleman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037171513","display_name":"David Easdown","orcid":"https://orcid.org/0000-0002-2296-2599","observed_orcids":["https://orcid.org/0000-0002-2296-2599"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Easdown","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9907000064849854,"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":0.9907000064849854,"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":0.0034000000450760126,"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/T12504","display_name":"Mathematics and Applications","score":0.0015999999595806003,"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/ring-decomposition","display_name":"ring decomposition","score":0.7699999809265137},{"id":"https://openalex.org/keywords/semidirect-products","display_name":"semidirect products","score":0.7490000128746033},{"id":"https://openalex.org/keywords/submonoids","display_name":"submonoids","score":0.7409999966621399},{"id":"https://openalex.org/keywords/subgroups","display_name":"subgroups","score":0.8629999756813049},{"id":"https://openalex.org/keywords/matrix-rings","display_name":"matrix rings","score":0.9430000185966492},{"id":"https://openalex.org/keywords/group-presentations","display_name":"group presentations","score":0.878000020980835},{"id":"https://openalex.org/keywords/rings-without-identity","display_name":"rings without identity","score":0.6869999766349792}],"concepts":[{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4628777503967285},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4160223603248596},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3633143901824951},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3220125436782837},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.12288084626197815},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.94.7047","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.94.7047","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/BAG/vol.43/no.1/b43h1eas.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W947610860","https://openalex.org/W1510024482","https://openalex.org/W1518454564","https://openalex.org/W1585649433","https://openalex.org/W1963809244","https://openalex.org/W1965803720","https://openalex.org/W1974390203","https://openalex.org/W1981559387","https://openalex.org/W1981684701","https://openalex.org/W2008445134","https://openalex.org/W2013964327","https://openalex.org/W2024293678","https://openalex.org/W2034469323","https://openalex.org/W2039235859","https://openalex.org/W2043655726","https://openalex.org/W2086897186","https://openalex.org/W2101718750","https://openalex.org/W2115751919","https://openalex.org/W2116283277","https://openalex.org/W2131613685","https://openalex.org/W2148893152","https://openalex.org/W2168674495","https://openalex.org/W2318629225","https://openalex.org/W2319169920","https://openalex.org/W2319687064","https://openalex.org/W2755887187","https://openalex.org/W2790029012","https://openalex.org/W3188230781"],"related_works":["https://openalex.org/W2329954183","https://openalex.org/W2614695495","https://openalex.org/W2490961771","https://openalex.org/W2154779527","https://openalex.org/W2313351431","https://openalex.org/W1981881295","https://openalex.org/W1964591047","https://openalex.org/W2104600994","https://openalex.org/W1494112935"],"abstract_inverted_index":{"Abstract.":[0],"We":[1],"consider":[2],"rings":[3,70],"S,":[4],"not":[5],"necessarily":[6],"with":[7],"1,":[8],"and":[9,16,48,62,85,103,109],"develop":[10],"a":[11],"decomposition":[12],"theory":[13,65],"for":[14,100],"submonoids":[15],"subgroups":[17],"of":[18,43,58,82],"(S,":[19,83,86],"\u25e6)":[20],"where":[21],"the":[22],"circle":[23],"operation":[24],"\u25e6":[25,30],"is":[26,66,75],"defined":[27],"by":[28],"x":[29,33],"y":[31,35],"=":[32,98],"+":[34],"\u2212":[36],"xy.":[37],"Decompositions":[38],"are":[39,90],"expressed":[40],"in":[41,56,80,93],"terms":[42,57,81],"internal":[44],"semidirect,":[45],"reverse":[46],"semidirect":[47],"general":[49],"products,":[50],"which":[51],"may":[52],"be":[53],"realised":[54],"externally":[55],"naturally":[59],"occurring":[60],"representations":[61],"antirepresentations.":[63],"The":[64],"applied":[67],"to":[68],"matrix":[69],"over":[71],"S":[72,74,97],"when":[73,96],"radical,":[76],"obtaining":[77],"group":[78],"presentations":[79],"+)":[84],"\u25e6).":[87],"Further":[88],"details":[89],"worked":[91],"out":[92],"special":[94],"cases":[95],"pZpt":[99],"p":[101],"prime":[102],"t":[104],"\u2265":[105],"3.":[106],"1.":[107],"Introduction":[108]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2025-10-27T00:00:00"}