Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W107327355', 'doi': 'https://doi.org/10.1007/978-94-009-3839-7_17', 'title': 'Cayley Theorems for Semigroups', 'display_name': 'Cayley Theorems for Semigroups', 'publication_year': 1987, 'publication_date': '1987-01-01', 'ids': {'openalex': 'https://openalex.org/W107327355', 'doi': 'https://doi.org/10.1007/978-94-009-3839-7_17', 'mag': '107327355'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/978-94-009-3839-7_17', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306463937', 'display_name': 'Springer eBooks', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_indexed_in_scopus': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310319965', 'host_organization_name': 'Springer Nature', 'host_organization_lineage': ['https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Springer Nature'], 'type': 'ebook platform'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'book-chapter', 'type_crossref': 'book-chapter', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5058534372', 'display_name': 'Mario Petrich', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I18014758', 'display_name': 'Simon Fraser University', 'ror': 'https://ror.org/0213rcc28', 'country_code': 'CA', 'type': 'education', 'lineage': ['https://openalex.org/I18014758']}], 'countries': ['CA'], 'is_corresponding': True, 'raw_author_name': 'Mario Petrich', 'raw_affiliation_strings': ['Department of Mathematics, Simon Fraser University, Burnaby, B.C., V5A 1S6, Canada'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, Simon Fraser University, Burnaby, B.C., V5A 1S6, Canada', 'institution_ids': ['https://openalex.org/I18014758']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5058534372'], 'corresponding_institution_ids': ['https://openalex.org/I18014758'], 'apc_list': None, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': False, 'cited_by_count': 4, 'citation_normalized_percentile': {'value': 0.609506, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 69, 'max': 71}, 'biblio': {'volume': None, 'issue': None, 'first_page': '133', 'last_page': '138'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11567', 'display_name': 'semigroups and automata theory', 'score': 0.8339, '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'}}, 'topics': [{'id': 'https://openalex.org/T11567', 'display_name': 'semigroups and automata theory', 'score': 0.8339, '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/T13400', 'display_name': 'Mathematical and Theoretical Analysis', 'score': 0.8002, '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/T13234', 'display_name': 'advanced mathematical theories', 'score': 0.7466, '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/krohn–rhodes-theory', 'display_name': 'Krohn–Rhodes theory', 'score': 0.73183393}, {'id': 'https://openalex.org/keywords/cayley-graph', 'display_name': 'Cayley graph', 'score': 0.65670687}, {'id': 'https://openalex.org/keywords/cayley-transform', 'display_name': 'Cayley transform', 'score': 0.553782}, {'id': 'https://openalex.org/keywords/cayleys-theorem', 'display_name': "Cayley's theorem", 'score': 0.4248969}], 'concepts': [{'id': 'https://openalex.org/C46149467', 'wikidata': 'https://www.wikidata.org/wiki/Q7574800', 'display_name': 'Special classes of semigroups', 'level': 3, 'score': 0.83749086}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.77980775}, {'id': 'https://openalex.org/C30397308', 'wikidata': 'https://www.wikidata.org/wiki/Q6438788', 'display_name': 'Krohn–Rhodes theory', 'level': 4, 'score': 0.73183393}, {'id': 'https://openalex.org/C120204988', 'wikidata': 'https://www.wikidata.org/wiki/Q859174', 'display_name': 'Cayley graph', 'level': 3, 'score': 0.65670687}, {'id': 'https://openalex.org/C207405024', 'wikidata': 'https://www.wikidata.org/wiki/Q207348', 'display_name': 'Semigroup', 'level': 2, 'score': 0.57914335}, {'id': 'https://openalex.org/C18586221', 'wikidata': 'https://www.wikidata.org/wiki/Q2778065', 'display_name': 'Cayley transform', 'level': 5, 'score': 0.553782}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.5189369}, {'id': 'https://openalex.org/C2777212361', 'wikidata': 'https://www.wikidata.org/wiki/Q5127848', 'display_name': 'Class (philosophy)', 'level': 2, 'score': 0.51627916}, {'id': 'https://openalex.org/C2780586882', 'wikidata': 'https://www.wikidata.org/wiki/Q7520643', 'display_name': 'Simple (philosophy)', 'level': 2, 'score': 0.47404385}, {'id': 'https://openalex.org/C207467116', 'wikidata': 'https://www.wikidata.org/wiki/Q4385666', 'display_name': 'Inverse', 'level': 2, 'score': 0.44033012}, {'id': 'https://openalex.org/C4093544', 'wikidata': 'https://www.wikidata.org/wiki/Q179208', 'display_name': "Cayley's theorem", 'level': 5, 'score': 0.4248969}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.38173398}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.36991882}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.08353096}, {'id': 'https://openalex.org/C154945302', 'wikidata': 'https://www.wikidata.org/wiki/Q11660', 'display_name': 'Artificial intelligence', 'level': 1, 'score': 0.02853027}, {'id': 'https://openalex.org/C132525143', 'wikidata': 'https://www.wikidata.org/wiki/Q141488', 'display_name': 'Graph', 'level': 2, '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/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/C22149727', 'wikidata': 'https://www.wikidata.org/wiki/Q7940747', 'display_name': 'Voltage graph', 'level': 4, 'score': 0.0}, {'id': 'https://openalex.org/C203776342', 'wikidata': 'https://www.wikidata.org/wiki/Q1378376', 'display_name': 'Line graph', 'level': 3, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/978-94-009-3839-7_17', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306463937', 'display_name': 'Springer eBooks', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_indexed_in_scopus': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310319965', 'host_organization_name': 'Springer Nature', 'host_organization_lineage': ['https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Springer Nature'], 'type': 'ebook platform'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 2, 'referenced_works': ['https://openalex.org/W2018559953', 'https://openalex.org/W2139912425'], 'related_works': ['https://openalex.org/W4298173932', 'https://openalex.org/W4213105785', 'https://openalex.org/W4205105712', 'https://openalex.org/W3144653330', 'https://openalex.org/W3139700519', 'https://openalex.org/W2963188491', 'https://openalex.org/W1986484118', 'https://openalex.org/W1983083559', 'https://openalex.org/W1968298352', 'https://openalex.org/W107327355'], 'abstract_inverted_index': None, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W107327355', 'counts_by_year': [], 'updated_date': '2025-01-20T20:08:38.516022', 'created_date': '2016-06-24'}