Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2030836261', 'doi': 'https://doi.org/10.1007/s002080050362', 'title': 'Intersection multiplicities over Gorenstein rings', 'display_name': 'Intersection multiplicities over Gorenstein rings', 'publication_year': 2000, 'publication_date': '2000-05-01', 'ids': {'openalex': 'https://openalex.org/W2030836261', 'doi': 'https://doi.org/10.1007/s002080050362', 'mag': '2030836261'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s002080050362', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S192217950', 'display_name': 'Mathematische Annalen', 'issn_l': '0025-5831', 'issn': ['0025-5831', '1432-1807'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, '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': '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://deepblue.lib.umich.edu/bitstream/2027.42/41934/1/208-317-1-155_03170155.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5082820216', 'display_name': 'Claudia Miller', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I27837315', 'display_name': 'University of Michigan–Ann Arbor', 'ror': 'https://ror.org/00jmfr291', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I27837315']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Claudia M. Miller', 'raw_affiliation_strings': ['Department of Mathematics, The University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, MI 48109–1109, USA (e-mail: [email protected], [email protected]), , US'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, The University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, MI 48109–1109, USA (e-mail: [email protected], [email protected]), , US', 'institution_ids': ['https://openalex.org/I27837315']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5102789338', 'display_name': 'Anurag K. Singh', 'orcid': 'https://orcid.org/0000-0002-3912-2393'}, 'institutions': [{'id': 'https://openalex.org/I27837315', 'display_name': 'University of Michigan–Ann Arbor', 'ror': 'https://ror.org/00jmfr291', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I27837315']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Anurag K. Singh', 'raw_affiliation_strings': ['Department of Mathematics, The University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, MI 48109–1109, USA (e-mail: [email protected], [email protected]), , US'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, The University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, MI 48109–1109, USA (e-mail: [email protected], [email protected]), , US', 'institution_ids': ['https://openalex.org/I27837315']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 2290, 'currency': 'EUR', 'value_usd': 2890, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 3.098, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 27, 'citation_normalized_percentile': {'value': 0.862705, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 87, 'max': 88}, 'biblio': {'volume': '317', 'issue': '1', 'first_page': '155', 'last_page': '171'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10287', 'display_name': 'Cluster Algebras and Triangulated Categories', 'score': 1.0, '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': 'Cluster Algebras and Triangulated Categories', 'score': 1.0, '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/T10061', 'display_name': 'Algebraic Geometry and Moduli Theory', 'score': 0.9999, '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': 'Monomial Ideals and Algebraic Properties', 'score': 0.9998, '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/complete-intersection', 'display_name': 'Complete intersection', 'score': 0.679667}, {'id': 'https://openalex.org/keywords/regularity-bounds', 'display_name': 'Regularity Bounds', 'score': 0.504999}, {'id': 'https://openalex.org/keywords/moduli-theory', 'display_name': 'Moduli Theory', 'score': 0.502547}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.76095104}, {'id': 'https://openalex.org/C37253', 'wikidata': 'https://www.wikidata.org/wiki/Q5156502', 'display_name': 'Complete intersection', 'level': 2, 'score': 0.679667}, {'id': 'https://openalex.org/C33676613', 'wikidata': 'https://www.wikidata.org/wiki/Q13415176', 'display_name': 'Dimension (graph theory)', 'level': 2, 'score': 0.6549115}, {'id': 'https://openalex.org/C142109727', 'wikidata': 'https://www.wikidata.org/wiki/Q1142704', 'display_name': 'Local ring', 'level': 3, 'score': 0.6484537}, {'id': 'https://openalex.org/C64543145', 'wikidata': 'https://www.wikidata.org/wiki/Q162942', 'display_name': 'Intersection (aeronautics)', 'level': 2, 'score': 0.5818626}, {'id': 'https://openalex.org/C2780378348', 'wikidata': 'https://www.wikidata.org/wiki/Q25351438', 'display_name': 'Ring (chemistry)', 'level': 2, 'score': 0.5489755}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.54483074}, {'id': 'https://openalex.org/C34388435', 'wikidata': 'https://www.wikidata.org/wiki/Q2267362', 'display_name': 'Bounded function', 'level': 2, 'score': 0.5437833}, {'id': 'https://openalex.org/C2780861071', 'wikidata': 'https://www.wikidata.org/wiki/Q1062934', 'display_name': 'Character (mathematics)', 'level': 2, 'score': 0.5064732}, {'id': 'https://openalex.org/C2777212361', 'wikidata': 'https://www.wikidata.org/wiki/Q5127848', 'display_name': 'Class (philosophy)', 'level': 2, 'score': 0.5054574}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.43417966}, {'id': 'https://openalex.org/C9652623', 'wikidata': 'https://www.wikidata.org/wiki/Q190109', 'display_name': 'Field (mathematics)', 'level': 2, 'score': 0.41824275}, {'id': 'https://openalex.org/C184992742', 'wikidata': 'https://www.wikidata.org/wiki/Q7243229', 'display_name': 'Prime (order theory)', 'level': 2, 'score': 0.41672596}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.35948163}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.1289948}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.119048595}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C178790620', 'wikidata': 'https://www.wikidata.org/wiki/Q11351', 'display_name': 'Organic chemistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C154945302', 'wikidata': 'https://www.wikidata.org/wiki/Q11660', 'display_name': 'Artificial intelligence', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C127413603', 'wikidata': 'https://www.wikidata.org/wiki/Q11023', 'display_name': 'Engineering', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C146978453', 'wikidata': 'https://www.wikidata.org/wiki/Q3798668', 'display_name': 'Aerospace engineering', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 5, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s002080050362', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S192217950', 'display_name': 'Mathematische Annalen', 'issn_l': '0025-5831', 'issn': ['0025-5831', '1432-1807'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, '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': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hdl.handle.net/2027.42/41934', 'pdf_url': 'http://deepblue.lib.umich.edu/bitstream/2027.42/41934/1/208-317-1-155_03170155.pdf', 'source': {'id': 'https://openalex.org/S4306400393', 'display_name': 'Deep Blue (University of Michigan)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I27837315', 'host_organization_name': 'University of Michigan–Ann Arbor', 'host_organization_lineage': ['https://openalex.org/I27837315'], 'host_organization_lineage_names': ['University of Michigan–Ann Arbor'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://surface.syr.edu/mat/10', 'pdf_url': 'https://surface.syr.edu/cgi/viewcontent.cgi?article=1087&context=mat', 'source': {'id': 'https://openalex.org/S4306402577', 'display_name': 'SURFACE: the Syracuse University Research Facility and Collaborative Environment (Syracuse University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I70983195', 'host_organization_name': 'Syracuse University', 'host_organization_lineage': ['https://openalex.org/I70983195'], 'host_organization_lineage_names': ['Syracuse University'], 'type': 'repository'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': None, 'pdf_url': 'https://arxiv.org/pdf/math/0210129v1.pdf', '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}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/math/0210129', 'pdf_url': 'https://arxiv.org/pdf/math/0210129', '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': 'https://hdl.handle.net/2027.42/41934', 'pdf_url': 'http://deepblue.lib.umich.edu/bitstream/2027.42/41934/1/208-317-1-155_03170155.pdf', 'source': {'id': 'https://openalex.org/S4306400393', 'display_name': 'Deep Blue (University of Michigan)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I27837315', 'host_organization_name': 'University of Michigan–Ann Arbor', 'host_organization_lineage': ['https://openalex.org/I27837315'], 'host_organization_lineage_names': ['University of Michigan–Ann Arbor'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 12, 'referenced_works': ['https://openalex.org/W1594914976', 'https://openalex.org/W1990648816', 'https://openalex.org/W2004787065', 'https://openalex.org/W2006021039', 'https://openalex.org/W2006958880', 'https://openalex.org/W2032163382', 'https://openalex.org/W2052681271', 'https://openalex.org/W2063228906', 'https://openalex.org/W2065599615', 'https://openalex.org/W2077999274', 'https://openalex.org/W2321773093', 'https://openalex.org/W2499571092'], 'related_works': ['https://openalex.org/W4387725540', 'https://openalex.org/W4382700114', 'https://openalex.org/W4300901382', 'https://openalex.org/W4293818650', 'https://openalex.org/W4287991114', 'https://openalex.org/W2995727719', 'https://openalex.org/W2065386375', 'https://openalex.org/W2054381763', 'https://openalex.org/W1642410760', 'https://openalex.org/W1532572863'], 'abstract_inverted_index': {'Let': [0], 'R': [1, 44, 66], 'be': [2, 21], 'a': [3, 11, 46, 50, 60, 63, 83, 91], 'complete': [4, 47], 'local': [5, 96], 'ring': [6, 43, 52, 65], 'of': [7, 14, 24, 53, 67, 82, 90], 'dimension': [8, 54, 68], 'd': [9], 'over': [10, 62], 'perfect': [12], 'field': [13], 'prime': [15], 'characteristic': [16], 'p,': [17], 'and': [18, 27, 89], 'let': [19], 'M': [20], 'an': [22, 80], 'R-module': [23], 'finite': [25, 28], 'length': [26], 'projective': [29], 'dimension.': [30], 'S.': [31], 'Dutta': [32], 'showed': [33], 'that': [34], 'the': [35, 42], 'equality': [36, 73], '$\\lim_{n\\to\\infty}\\frac{\\ell(F^n_R(M))}{p^{nd}}': [37], '=': [38], '\\ell(M)$': [39], 'holds': [40], 'when': [41], 'is': [45], 'intersection': [48], 'or': [49], 'Gorenstein': [51, 64], 'at': [55], 'most': [56], '3.': [57], 'We': [58], 'construct': [59], 'module': [61], 'five': [69], 'for': [70], 'which': [71], 'this': [72, 103], 'fails': [74], 'to': [75], 'hold.': [76], 'This': [77], 'then': [78], 'provides': [79], 'example': [81], 'nonzero': [84], 'Todd': [85], 'class': [86], '$\\tau_3(R)$': [87], ',': [88], 'bounded': [92], 'free': [93], 'complex': [94], 'whose': [95], 'Chern': [97], 'character': [98], 'does': [99], 'not': [100], 'vanish': [101], 'on': [102], 'class.': [104]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2030836261', 'counts_by_year': [{'year': 2017, 'cited_by_count': 1}, {'year': 2016, 'cited_by_count': 1}, {'year': 2015, 'cited_by_count': 1}, {'year': 2012, 'cited_by_count': 2}], 'updated_date': '2024-09-24T14:07:45.011683', 'created_date': '2016-06-24'}