{"id":"https://openalex.org/W2088257038","doi":"https://doi.org/10.1155/2013/150704","title":"Dimension Result for the Polynomial Algebra as a Module over the Steenrod Algebra","display_name":"Dimension Result for the Polynomial Algebra as a Module over the Steenrod Algebra","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2088257038","doi":"https://doi.org/10.1155/2013/150704","mag":"2088257038"},"language":"en","primary_location":{"id":"doi:10.1155/2013/150704","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/150704","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/150704.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2013/150704.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103064236","display_name":"Mbakiso F. Mothebe","orcid":"https://orcid.org/0000-0003-3734-8230"},"institutions":[{"id":"https://openalex.org/I157273133","display_name":"University of Botswana","ror":"https://ror.org/01encsj80","country_code":"BW","type":"education","lineage":["https://openalex.org/I157273133"]}],"countries":["BW"],"is_corresponding":true,"raw_author_name":"Mbakiso Fix Mothebe","raw_affiliation_strings":["Department of Mathematics, University of Botswana, Private Bag 00704, Gaborone"],"raw_orcid":"https://orcid.org/0000-0003-3734-8230","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Botswana, Private Bag 00704, Gaborone","institution_ids":["https://openalex.org/I157273133"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103064236"],"corresponding_institution_ids":["https://openalex.org/I157273133"],"apc_list":{"value":1240,"currency":"USD","value_usd":1240},"apc_paid":{"value":1240,"currency":"USD","value_usd":1240},"fwci":0.8031,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.69329873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9790999889373779,"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"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9790999889373779,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7747946381568909},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5621377825737},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5107576847076416},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4913758337497711},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4299491345882416},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.41267579793930054},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.329529732465744},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2663884162902832},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10422879457473755}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7747946381568909},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5621377825737},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5107576847076416},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4913758337497711},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4299491345882416},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.41267579793930054},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.329529732465744},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2663884162902832},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10422879457473755},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2013/150704","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/150704","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/150704.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:150704","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2013/150704.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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"},{"id":"pmh:oai:doaj.org/article:4e30236b4d114803b586e195e31b8385","is_oa":true,"landing_page_url":"https://doaj.org/article/4e30236b4d114803b586e195e31b8385","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":"International Journal of Mathematics and Mathematical Sciences, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/150704","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/150704","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/150704.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2088257038.pdf","grobid_xml":"https://content.openalex.org/works/W2088257038.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W170161805","https://openalex.org/W1540373783","https://openalex.org/W1920394204","https://openalex.org/W1969369598","https://openalex.org/W1991742102","https://openalex.org/W1992275741","https://openalex.org/W2050091710","https://openalex.org/W2062117975","https://openalex.org/W2100864874","https://openalex.org/W2142461847","https://openalex.org/W2170340602","https://openalex.org/W4236011740"],"related_works":["https://openalex.org/W1987895267","https://openalex.org/W2350519135","https://openalex.org/W2390619334","https://openalex.org/W2052190160","https://openalex.org/W2375327612","https://openalex.org/W2491835820","https://openalex.org/W2365099857","https://openalex.org/W4297848888","https://openalex.org/W2933449636","https://openalex.org/W4311344836"],"abstract_inverted_index":{"For":[0],"let":[1],"be":[2,89],"the":[3,12,29,32,35,50,60,75,92,98],"polynomial":[4],"algebra":[5,20],"in":[6,91],"variables":[7],"of":[8,14,31,34,39,45,62,65,69,74,100,102],"degree":[9,66,70,103],"one,":[10],"over":[11],"field":[13],"two":[15],"elements.":[16],"The":[17],"mod-2":[18],"Steenrod":[19],"acts":[21],"on":[22],"according":[23],"to":[24],"well-known":[25],"rules.":[26],"Let":[27],"denote":[28],"image":[30],"action":[33],"positively":[36],"graded":[37,57],"part":[38],"A":[40,67],"major":[41],"problem":[42],"is":[43,71,97],"that":[44,85],"determining":[46],"a":[47,72],"basis":[48],"for":[49,78],"quotient":[51],"vector":[52],"space":[53],"Both":[54],"and":[55,87],"are":[56],"where":[58,77,96],"denotes":[59],"set":[61],"homogeneous":[63],"polynomials":[64],"spike":[68],"monomial":[73],"form":[76,93],"each":[79],"In":[80],"this":[81],"paper":[82],"we":[83],"show":[84],"if":[86],"can":[88],"expressed":[90],"with":[94],"then":[95],"number":[99],"spikes":[101]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2016-06-24T00:00:00"}
