The Abelian Group in Mapping Perspective

Name: Work Video:
Duration: 3 min 30 s
Description: The Abelian group, also known as the exchange group, is a class of groups which satisfy the exchange law. This paper reviews Abelian groups from the perspective of mappings and gives sufficient and necessary conditions for a group to be an Abelian group under several special mappings.
Yuansheng Gao
{'id': 'https://openalex.org/W4380836961', 'doi': 'https://doi.org/10.25236/ajms.2023.040205', 'title': 'The Abelian Group in Mapping Perspective', 'display_name': 'The Abelian Group in Mapping Perspective', 'publication_year': 2023, 'publication_date': '2023-01-01', 'ids': {'openalex': 'https://openalex.org/W4380836961', 'doi': 'https://doi.org/10.25236/ajms.2023.040205'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.25236/ajms.2023.040205', 'pdf_url': 'http://francis-press.com/uploads/papers/QyrXQXk4b9RVo71f3OtstmIzY2amh7tMA9PQ3DFi.pdf', 'source': {'id': 'https://openalex.org/S4387283262', 'display_name': 'Academic Journal of Mathematical Sciences', 'issn_l': '2616-5805', 'issn': ['2616-5805'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'journal'}, 'license': None, 'license_id': None, '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': 'http://francis-press.com/uploads/papers/QyrXQXk4b9RVo71f3OtstmIzY2amh7tMA9PQ3DFi.pdf', 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5017414060', 'display_name': 'Yuansheng Gao', 'orcid': 'https://orcid.org/0000-0003-3278-8835'}, 'institutions': [{'id': 'https://openalex.org/I176808543', 'display_name': 'Liaoning Technical University', 'ror': 'https://ror.org/01n2bd587', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I176808543']}], 'countries': ['CN'], 'is_corresponding': True, 'raw_author_name': 'Yuansheng Gao', 'raw_affiliation_strings': ['College of Science, Liaoning Technical University, Fuxin, 123000, China'], 'affiliations': [{'raw_affiliation_string': 'College of Science, Liaoning Technical University, Fuxin, 123000, China', 'institution_ids': ['https://openalex.org/I176808543']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5017414060'], 'corresponding_institution_ids': ['https://openalex.org/I176808543'], 'apc_list': None, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 68}, 'biblio': {'volume': '4', 'issue': '2', 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12162', 'display_name': 'Cellular Automata and Applications', 'score': 0.7352, '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/T12162', 'display_name': 'Cellular Automata and Applications', 'score': 0.7352, '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/T12029', 'display_name': 'DNA and Biological Computing', 'score': 0.651, 'subfield': {'id': 'https://openalex.org/subfields/1312', 'display_name': 'Molecular Biology'}, 'field': {'id': 'https://openalex.org/fields/13', 'display_name': 'Biochemistry, Genetics and Molecular Biology'}, 'domain': {'id': 'https://openalex.org/domains/1', 'display_name': 'Life Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/free-abelian-group', 'display_name': 'Free abelian group', 'score': 0.44309887}], 'concepts': [{'id': 'https://openalex.org/C136170076', 'wikidata': 'https://www.wikidata.org/wiki/Q181296', 'display_name': 'Abelian group', 'level': 2, 'score': 0.90823925}, {'id': 'https://openalex.org/C163572010', 'wikidata': 'https://www.wikidata.org/wiki/Q2912125', 'display_name': 'G-module', 'level': 4, 'score': 0.7645581}, {'id': 'https://openalex.org/C12713177', 'wikidata': 'https://www.wikidata.org/wiki/Q1900281', 'display_name': 'Perspective (graphical)', 'level': 2, 'score': 0.7196419}, {'id': 'https://openalex.org/C2781311116', 'wikidata': 'https://www.wikidata.org/wiki/Q83306', 'display_name': 'Group (periodic table)', 'level': 2, 'score': 0.6896376}, {'id': 'https://openalex.org/C81008192', 'wikidata': 'https://www.wikidata.org/wiki/Q1017231', 'display_name': 'Elementary abelian group', 'level': 3, 'score': 0.6782439}, {'id': 'https://openalex.org/C170124329', 'wikidata': 'https://www.wikidata.org/wiki/Q592651', 'display_name': 'Non-abelian group', 'level': 4, 'score': 0.66632336}, {'id': 'https://openalex.org/C200681373', 'wikidata': 'https://www.wikidata.org/wiki/Q1260803', 'display_name': 'Rank of an abelian group', 'level': 4, 'score': 0.49284625}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.46775886}, {'id': 'https://openalex.org/C197623797', 'wikidata': 'https://www.wikidata.org/wiki/Q1454111', 'display_name': 'Free abelian group', 'level': 5, 'score': 0.44309887}, {'id': 'https://openalex.org/C2777212361', 'wikidata': 'https://www.wikidata.org/wiki/Q5127848', 'display_name': 'Class (philosophy)', 'level': 2, 'score': 0.43866473}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.42418975}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.38169503}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.29811966}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.15844819}, {'id': 'https://openalex.org/C154945302', 'wikidata': 'https://www.wikidata.org/wiki/Q11660', 'display_name': 'Artificial intelligence', 'level': 1, 'score': 0.107251585}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.06142506}, {'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/10.25236/ajms.2023.040205', 'pdf_url': 'http://francis-press.com/uploads/papers/QyrXQXk4b9RVo71f3OtstmIzY2amh7tMA9PQ3DFi.pdf', 'source': {'id': 'https://openalex.org/S4387283262', 'display_name': 'Academic Journal of Mathematical Sciences', 'issn_l': '2616-5805', 'issn': ['2616-5805'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.25236/ajms.2023.040205', 'pdf_url': 'http://francis-press.com/uploads/papers/QyrXQXk4b9RVo71f3OtstmIzY2amh7tMA9PQ3DFi.pdf', 'source': {'id': 'https://openalex.org/S4387283262', 'display_name': 'Academic Journal of Mathematical Sciences', 'issn_l': '2616-5805', 'issn': ['2616-5805'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [{'score': 0.61, 'display_name': 'Peace, justice, and strong institutions', 'id': 'https://metadata.un.org/sdg/16'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 7, 'referenced_works': ['https://openalex.org/W2091770425', 'https://openalex.org/W2171162943', 'https://openalex.org/W3081200114', 'https://openalex.org/W4230191592', 'https://openalex.org/W4280646951', 'https://openalex.org/W4297749115', 'https://openalex.org/W591591544'], 'related_works': ['https://openalex.org/W4247216989', 'https://openalex.org/W2917437667', 'https://openalex.org/W2910936094', 'https://openalex.org/W2375875135', 'https://openalex.org/W2334395775', 'https://openalex.org/W2317222639', 'https://openalex.org/W2023033882', 'https://openalex.org/W2009465652', 'https://openalex.org/W1999189963', 'https://openalex.org/W1034923237'], 'abstract_inverted_index': {'The': [0], 'Abelian': [1, 22, 41], 'group,': [2, 8], 'also': [3], 'known': [4], 'as': [5], 'the': [6, 16, 25], 'exchange': [7, 17], 'is': [9], 'a': [10, 36], 'class': [11], 'of': [12, 27], 'groups': [13, 23], 'which': [14], 'satisfy': [15], 'law.': [18], 'This': [19], 'paper': [20], 'reviews': [21], 'from': [24], 'perspective': [26], 'mappings': [28], 'and': [29, 32], 'gives': [30], 'sufficient': [31], 'necessary': [33], 'conditions': [34], 'for': [35], 'group': [37, 42], 'to': [38], 'be': [39], 'an': [40], 'under': [43], 'several': [44], 'special': [45], 'mappings.': [46]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4380836961', 'counts_by_year': [], 'updated_date': '2024-12-13T08:32:59.729516', 'created_date': '2023-06-16'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
