Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W1994431500', 'doi': 'https://doi.org/10.1016/s0012-9593(03)00014-4', 'title': 'André–Quillen homology of algebra retracts', 'display_name': 'André–Quillen homology of algebra retracts', 'publication_year': 2003, 'publication_date': '2003-05-01', 'ids': {'openalex': 'https://openalex.org/W1994431500', 'doi': 'https://doi.org/10.1016/s0012-9593(03)00014-4', 'mag': '1994431500'}, 'language': 'fr', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1016/s0012-9593(03)00014-4', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S182617021', 'display_name': 'Annales Scientifiques de l École Normale Supérieure', 'issn_l': '0012-9593', 'issn': ['0012-9593', '1873-2151'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310311320', 'host_organization_name': 'Société Mathématique de France', 'host_organization_lineage': ['https://openalex.org/P4310311320'], 'host_organization_lineage_names': ['Société Mathématique de France'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'http://www.numdam.org/item/10.1016/S0012-9593(03)00014-4.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5013744220', 'display_name': 'LL Avramov', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I114395901', 'display_name': 'University of Nebraska–Lincoln', 'ror': 'https://ror.org/043mer456', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I114395901']}, {'id': 'https://openalex.org/I219193219', 'display_name': 'Purdue University West Lafayette', 'ror': 'https://ror.org/02dqehb95', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I219193219']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'L AVRAMOV', 'raw_affiliation_strings': ['Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA Current address: Department of Mathematics, University of Nebraska, Lincoln, NE 68588, USA'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA Current address: Department of Mathematics, University of Nebraska, Lincoln, NE 68588, USA', 'institution_ids': ['https://openalex.org/I114395901', 'https://openalex.org/I219193219']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5077663448', 'display_name': 'Satish Iyengar', 'orcid': 'https://orcid.org/0000-0002-9329-6853'}, 'institutions': [{'id': 'https://openalex.org/I76835614', 'display_name': 'University of Missouri', 'ror': 'https://ror.org/02ymw8z06', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I76835614']}, {'id': 'https://openalex.org/I91136226', 'display_name': 'University of Sheffield', 'ror': 'https://ror.org/05krs5044', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I91136226']}], 'countries': ['GB', 'US'], 'is_corresponding': False, 'raw_author_name': 'S IYENGAR', 'raw_affiliation_strings': ['Pure Mathematics, Hicks Building, University of Sheffield, Sheffield S3 7RH, UK Current address: Department of Mathematics, University of Missouri, Columbia, MO 65201, USA'], 'affiliations': [{'raw_affiliation_string': 'Pure Mathematics, Hicks Building, University of Sheffield, Sheffield S3 7RH, UK Current address: Department of Mathematics, University of Missouri, Columbia, MO 65201, USA', 'institution_ids': ['https://openalex.org/I76835614', 'https://openalex.org/I91136226']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 4, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.713, 'has_fulltext': False, 'cited_by_count': 12, 'citation_normalized_percentile': {'value': 0.706241, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 81, 'max': 82}, 'biblio': {'volume': '36', 'issue': '3', 'first_page': '431', 'last_page': '462'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10287', 'display_name': 'Algebraic structures and combinatorial models', 'score': 0.9996, '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': 0.9996, '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/T10896', 'display_name': 'Homotopy and Cohomology in Algebraic Topology', 'score': 0.9993, '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/T11673', 'display_name': 'Advanced Topics in Algebra', 'score': 0.9989, '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'}}], 'keywords': [{'id': 'https://openalex.org/keywords/homology', 'display_name': 'Homology', 'score': 0.578644}, {'id': 'https://openalex.org/keywords/noetherian-ring', 'display_name': 'Noetherian ring', 'score': 0.4213823}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.78094745}, {'id': 'https://openalex.org/C156772000', 'wikidata': 'https://www.wikidata.org/wiki/Q864475', 'display_name': 'Functor', 'level': 2, 'score': 0.6348436}, {'id': 'https://openalex.org/C4042151', 'wikidata': 'https://www.wikidata.org/wiki/Q215111', 'display_name': 'Homomorphism', 'level': 2, 'score': 0.59834635}, {'id': 'https://openalex.org/C165525559', 'wikidata': 'https://www.wikidata.org/wiki/Q224180', 'display_name': 'Homology (biology)', 'level': 3, 'score': 0.578644}, {'id': 'https://openalex.org/C2780990831', 'wikidata': 'https://www.wikidata.org/wiki/Q319141', 'display_name': 'Conjecture', 'level': 2, 'score': 0.54766583}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.522629}, {'id': 'https://openalex.org/C2779057376', 'wikidata': 'https://www.wikidata.org/wiki/Q3342676', 'display_name': 'Noetherian', 'level': 3, 'score': 0.49271396}, {'id': 'https://openalex.org/C2777726979', 'wikidata': 'https://www.wikidata.org/wiki/Q582271', 'display_name': 'Noetherian ring', 'level': 3, 'score': 0.4213823}, {'id': 'https://openalex.org/C183778304', 'wikidata': 'https://www.wikidata.org/wiki/Q165474', 'display_name': 'Commutative property', 'level': 2, 'score': 0.4120093}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.35289162}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.3491404}, {'id': 'https://openalex.org/C162860070', 'wikidata': 'https://www.wikidata.org/wiki/Q142140', 'display_name': 'Finitely-generated abelian group', 'level': 2, 'score': 0.33380812}, {'id': 'https://openalex.org/C55493867', 'wikidata': 'https://www.wikidata.org/wiki/Q7094', 'display_name': 'Biochemistry', 'level': 1, '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/C104317684', 'wikidata': 'https://www.wikidata.org/wiki/Q7187', 'display_name': 'Gene', 'level': 2, 'score': 0.0}], 'mesh': [], 'locations_count': 3, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1016/s0012-9593(03)00014-4', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S182617021', 'display_name': 'Annales Scientifiques de l École Normale Supérieure', 'issn_l': '0012-9593', 'issn': ['0012-9593', '1873-2151'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310311320', 'host_organization_name': 'Société Mathématique de France', 'host_organization_lineage': ['https://openalex.org/P4310311320'], 'host_organization_lineage_names': ['Société Mathématique de France'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://www.numdam.org/articles/10.1016/S0012-9593(03)00014-4/', 'pdf_url': 'http://www.numdam.org/item/10.1016/S0012-9593(03)00014-4.pdf', 'source': {'id': 'https://openalex.org/S4306402264', 'display_name': 'French digital mathematics library (Numdam)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I70900168', 'host_organization_name': 'Université Savoie Mont Blanc', 'host_organization_lineage': ['https://openalex.org/I70900168'], 'host_organization_lineage_names': ['Université Savoie Mont Blanc'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/math/0210037', 'pdf_url': 'http://arxiv.org/pdf/math/0210037', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'http://www.numdam.org/articles/10.1016/S0012-9593(03)00014-4/', 'pdf_url': 'http://www.numdam.org/item/10.1016/S0012-9593(03)00014-4.pdf', 'source': {'id': 'https://openalex.org/S4306402264', 'display_name': 'French digital mathematics library (Numdam)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I70900168', 'host_organization_name': 'Université Savoie Mont Blanc', 'host_organization_lineage': ['https://openalex.org/I70900168'], 'host_organization_lineage_names': ['Université Savoie Mont Blanc'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 21, 'referenced_works': ['https://openalex.org/W103487821', 'https://openalex.org/W1337302', 'https://openalex.org/W1537795765', 'https://openalex.org/W155431822', 'https://openalex.org/W1587338598', 'https://openalex.org/W1600090509', 'https://openalex.org/W1638655704', 'https://openalex.org/W1966569384', 'https://openalex.org/W1978852029', 'https://openalex.org/W2019893652', 'https://openalex.org/W2047413546', 'https://openalex.org/W2059460865', 'https://openalex.org/W2065870104', 'https://openalex.org/W2069525742', 'https://openalex.org/W2071347824', 'https://openalex.org/W2125401081', 'https://openalex.org/W2140583180', 'https://openalex.org/W2316009494', 'https://openalex.org/W2319499103', 'https://openalex.org/W2534287436', 'https://openalex.org/W71296093'], 'related_works': ['https://openalex.org/W4382363823', 'https://openalex.org/W4378498602', 'https://openalex.org/W4297848538', 'https://openalex.org/W4295837907', 'https://openalex.org/W4226156931', 'https://openalex.org/W3154785237', 'https://openalex.org/W3100127102', 'https://openalex.org/W2142230314', 'https://openalex.org/W1967526909', 'https://openalex.org/W1695353777'], 'abstract_inverted_index': {'Given': [0], 'a': [1, 41, 59, 100], 'homomorphism': [2, 42], 'of': [3, 43, 69], 'commutative': [4], 'noetherian': [5], 'rings': [6, 44], 'ϕ:R→S,': [7], 'Daniel': [8, 98], 'Quillen': [9, 99], 'conjectured': [10], 'in': [11, 51], '1970': [12, 103], 'that': [13, 38, 47, 56], 'if': [14], 'the': [15, 32, 35, 82], 'André–Quillen': [16], 'homology': [17], 'functors': [18], 'Dn(S∣R;−)': [19, 108], 'vanish': [20, 26], 'for': [21, 27, 64, 80], 'all': [22, 28, 76], 'n⪢0,': [23, 115], 'then': [24], 'they': [25], 'n⩾3.': [29, 122], 'We': [30], 'prove': [31], 'conjecture': [33, 126], 'under': [34], 'additional': [36], 'hypothesis': [37], 'there': [39], 'exists': [40], 'ψ:S→R': [45, 135], 'such': [46], 'ϕ∘ψ=idS.': [48, 138], 'More': [49], 'precisely,': [50], 'this': [52], 'case': [53], 'we': [54, 74], 'show': [55], 'ψ': [57, 147], 'is': [58, 85], 'complete': [60], 'intersection': [61], 'at': [62], 'ϕ−1(n)': [63, 152], 'every': [65], 'prime': [66], 'ideal': [67], 'n': [68, 157], 'S.': [70, 159], 'Using': [71], 'these': [72], 'results,': [73], 'describe': [75], 'algebra': [77, 83], 'retracts': [78], 'S→R→S': [79, 170], 'which': [81], 'Tor•R(S,S)': [84, 174], 'finitely': [86], 'generated': [87], 'over': [88], 'Tor0R(S,S)=S.': [89, 179], 'Étant': [90], 'donné': [91], 'un': [92, 132], 'homomorphisme': [93, 133], 'ϕ:R→S': [94], "d'anneaux": [95, 134], 'commutatifs': [96], 'noethériens,': [97], 'conjecturé': [101], 'en': [102, 151], 'que': [104, 137, 143], 'si': [105], 'les': [106, 167], 'foncteurs': [107], "d'homologie": [109], "d'André–Quillen": [110], 'sont': [111, 118], 'nuls': [112, 119], 'pour': [113, 120, 153, 171], 'tout': [114, 121, 154], 'alors': [116], 'ils': [117], 'Nous': [123], 'démontrons': [124], 'cette': [125], 'sous': [127], "l'hypothèse": [128], 'supplémentaire': [129], "qu'il": [130], 'existe': [131], 'tel': [136], 'Plus': [139], 'précisément,': [140], 'nous': [141, 164], 'montrons': [142], 'dans': [144], 'ce': [145], 'cas': [146], 'est': [148, 175], "d'intersection": [149], 'complète': [150], 'idéal': [155], 'premier': [156], 'de': [158], 'En': [160], 'utilisant': [161], 'ces': [162], 'résultats,': [163], 'décrivons': [165], 'toutes': [166], 'algèbres': [168], 'scindées': [169], 'lesquelles': [172], "l'algèbre": [173], 'finiment': [176], 'engendrée': [177], 'sur': [178]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1994431500', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2023, 'cited_by_count': 2}, {'year': 2021, 'cited_by_count': 1}, {'year': 2016, 'cited_by_count': 2}, {'year': 2012, 'cited_by_count': 1}], 'updated_date': '2024-12-08T17:57:44.094295', 'created_date': '2016-06-24'}