Publication Information

{'id': 'https://openalex.org/W2608269246', 'doi': None, 'title': 'Galois Extensions with a Galois Commutator Subring', 'display_name': 'Galois Extensions with a Galois Commutator Subring', 'publication_year': 2009, 'publication_date': '2009-01-01', 'ids': {'openalex': 'https://openalex.org/W2608269246', 'mag': '2608269246'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'http://www.m-hikari.com/ija/ija-password-2009/ija-password17-20-2009/xueIJA17-20-2009.pdf', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': [], '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/A5082041696', 'display_name': 'George Szeto', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I24648388', 'display_name': 'Bradley University', 'ror': 'https://ror.org/04kmeaw70', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I24648388']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'George Szeto', 'raw_affiliation_strings': ['Bradley Univ.#TAB#'], 'affiliations': [{'raw_affiliation_string': 'Bradley Univ.#TAB#', 'institution_ids': ['https://openalex.org/I24648388']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5078753749', 'display_name': 'Lianyong Xue', 'orcid': 'https://orcid.org/0000-0001-5896-9234'}, 'institutions': [{'id': 'https://openalex.org/I24648388', 'display_name': 'Bradley University', 'ror': 'https://ror.org/04kmeaw70', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I24648388']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Lianyong Xue', 'raw_affiliation_strings': ['Bradley Univ.#TAB#'], 'affiliations': [{'raw_affiliation_string': 'Bradley Univ.#TAB#', 'institution_ids': ['https://openalex.org/I24648388']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.289, 'has_fulltext': False, 'cited_by_count': 1, 'citation_normalized_percentile': {'value': 0.297518, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 64, 'max': 71}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10287', 'display_name': 'Algebraic structures and combinatorial models', 'score': 0.9978, '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'}}, 'topics': [{'id': 'https://openalex.org/T10287', 'display_name': 'Algebraic structures and combinatorial models', 'score': 0.9978, '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'}}, {'id': 'https://openalex.org/T12069', 'display_name': 'Commutative Algebra and Its Applications', 'score': 0.9958, '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/T10061', 'display_name': 'Algebraic Geometry and Number Theory', 'score': 0.9947, '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/subring', 'display_name': 'Subring', 'score': 0.51578236}], 'concepts': [{'id': 'https://openalex.org/C67536143', 'wikidata': 'https://www.wikidata.org/wiki/Q730384', 'display_name': 'Galois group', 'level': 2, 'score': 0.8725971}, {'id': 'https://openalex.org/C35435516', 'wikidata': 'https://www.wikidata.org/wiki/Q5370016', 'display_name': 'Embedding problem', 'level': 3, 'score': 0.8141416}, {'id': 'https://openalex.org/C78562435', 'wikidata': 'https://www.wikidata.org/wiki/Q766522', 'display_name': 'Fundamental theorem of Galois theory', 'level': 4, 'score': 0.81201154}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.7994324}, {'id': 'https://openalex.org/C182349385', 'wikidata': 'https://www.wikidata.org/wiki/Q382839', 'display_name': 'Galois cohomology', 'level': 3, 'score': 0.78540003}, {'id': 'https://openalex.org/C26204071', 'wikidata': 'https://www.wikidata.org/wiki/Q2020004', 'display_name': 'Galois extension', 'level': 3, 'score': 0.7774129}, {'id': 'https://openalex.org/C57637645', 'wikidata': 'https://www.wikidata.org/wiki/Q318705', 'display_name': 'Abelian extension', 'level': 3, 'score': 0.75572187}, {'id': 'https://openalex.org/C145899342', 'wikidata': 'https://www.wikidata.org/wiki/Q3427418', 'display_name': 'Galois module', 'level': 2, 'score': 0.69943506}, {'id': 'https://openalex.org/C197968787', 'wikidata': 'https://www.wikidata.org/wiki/Q2383624', 'display_name': 'Differential Galois theory', 'level': 4, 'score': 0.51629657}, {'id': 'https://openalex.org/C21714298', 'wikidata': 'https://www.wikidata.org/wiki/Q929536', 'display_name': 'Subring', 'level': 3, 'score': 0.51578236}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.43096268}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.3976508}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.093685895}, {'id': 'https://openalex.org/C2780378348', 'wikidata': 'https://www.wikidata.org/wiki/Q25351438', 'display_name': 'Ring (chemistry)', 'level': 2, 'score': 0.064798504}, {'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': [{'is_oa': False, 'landing_page_url': 'http://www.m-hikari.com/ija/ija-password-2009/ija-password17-20-2009/xueIJA17-20-2009.pdf', 'pdf_url': None, 'source': None, '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': 7, 'referenced_works': ['https://openalex.org/W1552705010', 'https://openalex.org/W1589791546', 'https://openalex.org/W1605232220', 'https://openalex.org/W1971629547', 'https://openalex.org/W1998979737', 'https://openalex.org/W2009913677', 'https://openalex.org/W2087929114'], 'related_works': ['https://openalex.org/W2962735649', 'https://openalex.org/W2809815836', 'https://openalex.org/W2613914349', 'https://openalex.org/W2513122531', 'https://openalex.org/W2470208452', 'https://openalex.org/W221728974', 'https://openalex.org/W2158049816', 'https://openalex.org/W2134632890', 'https://openalex.org/W2130340786', 'https://openalex.org/W2102320443', 'https://openalex.org/W2076408465', 'https://openalex.org/W2075063310', 'https://openalex.org/W2045538252', 'https://openalex.org/W2044494398', 'https://openalex.org/W2029537060', 'https://openalex.org/W2004192809', 'https://openalex.org/W1991966614', 'https://openalex.org/W1989037175', 'https://openalex.org/W1983563541', 'https://openalex.org/W1969793882'], 'abstract_inverted_index': {'Let': [0], 'B': [1, 7, 18, 88, 96, 121, 129, 131, 139, 143], 'be': [2, 172], 'a': [3, 35, 58, 92, 110, 123, 158], 'Galois': [4, 10, 36, 43, 59, 65, 93, 99, 127, 135, 146, 180, 185, 188, 193], 'extension': [5, 37, 60, 94], 'of': [6, 17, 26, 39, 61, 95, 125, 179], 'G': [8, 19, 27, 41, 63, 78, 89, 97, 118, 132, 140, 144, 166], 'with': [9, 42, 64, 71, 98, 105, 134, 145, 152], 'group': [11, 44, 66, 100, 136, 147], 'G,': [12], 'Δ': [13, 38, 40, 56, 62, 90, 108, 117, 133, 141, 156, 165], 'the': [14, 24, 50], 'commutator': [15], 'subring': [16], 'in': [20], 'B,': [21], 'and': [22, 69, 103, 107, 113, 138, 150, 161, 190], 'G|Δ': [23], 'restriction': [25], 'to': [28], 'Δ.': [29], 'Equivalent': [30], 'conditions': [31], 'are': [32, 53], 'given': [33], 'for': [34, 82, 174], 'G|Δ.': [45], 'It': [46], 'is': [47, 57, 91, 109, 122, 157], 'shown': [48], 'that': [49, 155], 'following': [51], 'statements': [52], 'equivalent:': [54], '(1)': [55], 'induced': [67, 101, 148], 'by': [68, 102, 149], 'isomorphic': [70, 104, 151], 'G/N': [72, 106, 153], 'where': [73], 'N': [74, 137], '=': [75], '{g': [76], '∈': [77, 85], '|g(x': [79], ')=': [80], 'x': [81, 84], 'all': [83], 'Δ}.': [86], '(2)': [87], 'finitely': [111, 159], 'generated': [112, 160], 'projective': [114, 162], 'module': [115, 163], 'over': [116, 164], '.': [119, 167], '(3)': [120], 'composition': [124], 'two': [126], 'extensions:': [128], '⊃': [130, 142], 'such': [154, 182], 'Consequently,': [168], 'more': [169], 'results': [170], 'can': [171], 'derived': [173], 'several': [175], 'well': [176], 'known': [177], 'classes': [178], 'extensions': [181], 'as': [183], 'DeMeyer-Kanzaki': [184], 'extensions,': [186, 189], 'Azumaya': [187], 'Hirata': [191], 'separable': [192], 'extensions.': [194]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2608269246', 'counts_by_year': [{'year': 2012, 'cited_by_count': 1}], 'updated_date': '2024-12-11T18:33:11.315398', 'created_date': '2017-05-05'}