Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2006610312', 'doi': 'https://doi.org/10.1016/j.jmaa.2006.02.084', 'title': 'Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative', 'display_name': 'Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative', 'publication_year': 2006, 'publication_date': '2006-04-18', 'ids': {'openalex': 'https://openalex.org/W2006610312', 'doi': 'https://doi.org/10.1016/j.jmaa.2006.02.084', 'mag': '2006610312'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1016/j.jmaa.2006.02.084', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S151579836', 'display_name': 'Journal of Mathematical Analysis and Applications', 'issn_l': '0022-247X', 'issn': ['0022-247X', '1096-0813'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320990', 'host_organization_name': 'Elsevier BV', 'host_organization_lineage': ['https://openalex.org/P4310320990'], 'host_organization_lineage_names': ['Elsevier BV'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'https://doi.org/10.1016/j.jmaa.2006.02.084', 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5046066523', 'display_name': 'Osamu Hatori', 'orcid': 'https://orcid.org/0000-0002-4338-1355'}, 'institutions': [{'id': 'https://openalex.org/I71395657', 'display_name': 'Niigata University', 'ror': 'https://ror.org/04ww21r56', 'country_code': 'JP', 'type': 'education', 'lineage': ['https://openalex.org/I71395657']}], 'countries': ['JP'], 'is_corresponding': False, 'raw_author_name': 'Osamu Hatori', 'raw_affiliation_strings': ['Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, JAPAN'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, JAPAN', 'institution_ids': ['https://openalex.org/I71395657']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5028210923', 'display_name': 'Takeshi Miura', 'orcid': 'https://orcid.org/0000-0003-4125-5029'}, 'institutions': [{'id': 'https://openalex.org/I112524849', 'display_name': 'Yamagata University', 'ror': 'https://ror.org/00xy44n04', 'country_code': 'JP', 'type': 'education', 'lineage': ['https://openalex.org/I112524849']}], 'countries': ['JP'], 'is_corresponding': False, 'raw_author_name': 'Takeshi Miura', 'raw_affiliation_strings': ['Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yonezawa 992‐8510, Japan'], 'affiliations': [{'raw_affiliation_string': 'Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yonezawa 992‐8510, Japan', 'institution_ids': ['https://openalex.org/I112524849']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5004971760', 'display_name': 'Hiroyuki Takagi', 'orcid': 'https://orcid.org/0000-0002-4999-905X'}, 'institutions': [{'id': 'https://openalex.org/I137975476', 'display_name': 'Shinshu University', 'ror': 'https://ror.org/0244rem06', 'country_code': 'JP', 'type': 'education', 'lineage': ['https://openalex.org/I137975476']}], 'countries': ['JP'], 'is_corresponding': False, 'raw_author_name': 'Hiroyuki Takagi', 'raw_affiliation_strings': ['Department of Mathematical Sciences, Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematical Sciences, Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan', 'institution_ids': ['https://openalex.org/I137975476']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 3, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 3070, 'currency': 'USD', 'value_usd': 3070, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 7.756, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 50, 'citation_normalized_percentile': {'value': 0.938366, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 93, 'max': 94}, 'biblio': {'volume': '326', 'issue': '1', 'first_page': '281', 'last_page': '296'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11673', 'display_name': 'Advanced Topics in Algebra', 'score': 0.9997, '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/T11673', 'display_name': 'Advanced Topics in Algebra', 'score': 0.9997, '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/T11545', 'display_name': 'Advanced Banach Space Theory', 'score': 0.9995, '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/T10899', 'display_name': 'Advanced Operator Algebra Research', 'score': 0.9995, '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/surjective-function', 'display_name': 'Surjective function', 'score': 0.84565127}, {'id': 'https://openalex.org/keywords/unital', 'display_name': 'Unital', 'score': 0.8179961}, {'id': 'https://openalex.org/keywords/banach-algebra', 'display_name': 'Banach algebra', 'score': 0.75869656}, {'id': 'https://openalex.org/keywords/isomorphism', 'display_name': 'Isomorphism (crystallography)', 'score': 0.5955991}, {'id': 'https://openalex.org/keywords/linear-map', 'display_name': 'Linear map', 'score': 0.45217636}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.89691997}, {'id': 'https://openalex.org/C119238805', 'wikidata': 'https://www.wikidata.org/wiki/Q229102', 'display_name': 'Surjective function', 'level': 2, 'score': 0.84565127}, {'id': 'https://openalex.org/C160873635', 'wikidata': 'https://www.wikidata.org/wiki/Q17148807', 'display_name': 'Unital', 'level': 3, 'score': 0.8179961}, {'id': 'https://openalex.org/C2781106287', 'wikidata': 'https://www.wikidata.org/wiki/Q806066', 'display_name': 'Banach algebra', 'level': 3, 'score': 0.75869656}, {'id': 'https://openalex.org/C183778304', 'wikidata': 'https://www.wikidata.org/wiki/Q165474', 'display_name': 'Commutative property', 'level': 2, 'score': 0.7387681}, {'id': 'https://openalex.org/C42747912', 'wikidata': 'https://www.wikidata.org/wiki/Q1048447', 'display_name': 'Multiplicative function', 'level': 2, 'score': 0.6678878}, {'id': 'https://openalex.org/C203436722', 'wikidata': 'https://www.wikidata.org/wiki/Q902950', 'display_name': 'Isomorphism (crystallography)', 'level': 3, 'score': 0.5955991}, {'id': 'https://openalex.org/C156778621', 'wikidata': 'https://www.wikidata.org/wiki/Q1365748', 'display_name': 'Spectrum (functional analysis)', 'level': 2, 'score': 0.5321089}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.5168886}, {'id': 'https://openalex.org/C48659774', 'wikidata': 'https://www.wikidata.org/wiki/Q4907197', 'display_name': 'Bijection, injection and surjection', 'level': 3, 'score': 0.470485}, {'id': 'https://openalex.org/C2780586882', 'wikidata': 'https://www.wikidata.org/wiki/Q7520643', 'display_name': 'Simple (philosophy)', 'level': 2, 'score': 0.45913532}, {'id': 'https://openalex.org/C49766605', 'wikidata': 'https://www.wikidata.org/wiki/Q207643', 'display_name': 'Linear map', 'level': 2, 'score': 0.45217636}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.4044436}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.29967612}, {'id': 'https://openalex.org/C132954091', 'wikidata': 'https://www.wikidata.org/wiki/Q194397', 'display_name': 'Banach space', 'level': 2, 'score': 0.21000046}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.13918713}, {'id': 'https://openalex.org/C24424167', 'wikidata': 'https://www.wikidata.org/wiki/Q180907', 'display_name': 'Bijection', 'level': 2, 'score': 0.12769055}, {'id': 'https://openalex.org/C8010536', 'wikidata': 'https://www.wikidata.org/wiki/Q160398', 'display_name': 'Crystallography', 'level': 1, 'score': 0.07087311}, {'id': 'https://openalex.org/C138885662', 'wikidata': 'https://www.wikidata.org/wiki/Q5891', 'display_name': 'Philosophy', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C115624301', 'wikidata': 'https://www.wikidata.org/wiki/Q895901', 'display_name': 'Crystal structure', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, '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/C111472728', 'wikidata': 'https://www.wikidata.org/wiki/Q9471', 'display_name': 'Epistemology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1016/j.jmaa.2006.02.084', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S151579836', 'display_name': 'Journal of Mathematical Analysis and Applications', 'issn_l': '0022-247X', 'issn': ['0022-247X', '1096-0813'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320990', 'host_organization_name': 'Elsevier BV', 'host_organization_lineage': ['https://openalex.org/P4310320990'], 'host_organization_lineage_names': ['Elsevier BV'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1016/j.jmaa.2006.02.084', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S151579836', 'display_name': 'Journal of Mathematical Analysis and Applications', 'issn_l': '0022-247X', 'issn': ['0022-247X', '1096-0813'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320990', 'host_organization_name': 'Elsevier BV', 'host_organization_lineage': ['https://openalex.org/P4310320990'], 'host_organization_lineage_names': ['Elsevier BV'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [{'funder': 'https://openalex.org/F4320320912', 'funder_display_name': 'Ministry of Education, Culture, Sports, Science and Technology', 'award_id': None}], 'datasets': [], 'versions': [], 'referenced_works_count': 23, 'referenced_works': ['https://openalex.org/W1503122565', 'https://openalex.org/W1570752937', 'https://openalex.org/W1637991375', 'https://openalex.org/W1760342711', 'https://openalex.org/W1893256632', 'https://openalex.org/W1911299984', 'https://openalex.org/W1969792787', 'https://openalex.org/W2014448158', 'https://openalex.org/W2023163276', 'https://openalex.org/W2030175365', 'https://openalex.org/W2042466376', 'https://openalex.org/W2044504831', 'https://openalex.org/W2052100431', 'https://openalex.org/W2063343862', 'https://openalex.org/W2064122467', 'https://openalex.org/W2065091800', 'https://openalex.org/W2066514739', 'https://openalex.org/W2082534750', 'https://openalex.org/W2087040655', 'https://openalex.org/W2093958335', 'https://openalex.org/W2123818598', 'https://openalex.org/W2161907239', 'https://openalex.org/W4245659721'], 'related_works': ['https://openalex.org/W4300985044', 'https://openalex.org/W4300839745', 'https://openalex.org/W2963674572', 'https://openalex.org/W2963624937', 'https://openalex.org/W2735896492', 'https://openalex.org/W2294117133', 'https://openalex.org/W2293397776', 'https://openalex.org/W2056426854', 'https://openalex.org/W1985361210', 'https://openalex.org/W1573701756'], 'abstract_inverted_index': None, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2006610312', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2023, 'cited_by_count': 2}, {'year': 2022, 'cited_by_count': 3}, {'year': 2020, 'cited_by_count': 1}, {'year': 2019, 'cited_by_count': 2}, {'year': 2018, 'cited_by_count': 6}, {'year': 2015, 'cited_by_count': 3}, {'year': 2014, 'cited_by_count': 2}, {'year': 2013, 'cited_by_count': 2}, {'year': 2012, 'cited_by_count': 2}], 'updated_date': '2024-12-09T14:44:36.846464', 'created_date': '2016-06-24'}