{"id":"https://openalex.org/W2042488067","doi":"https://doi.org/10.1142/s0218196712500403","title":"ON BOUNDING MEASURES OF PRIMENESS IN INTEGRAL DOMAINS","display_name":"ON BOUNDING MEASURES OF PRIMENESS IN INTEGRAL DOMAINS","publication_year":2012,"publication_date":"2012-04-18","ids":{"openalex":"https://openalex.org/W2042488067","doi":"https://doi.org/10.1142/s0218196712500403","mag":"2042488067"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196712500403","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500403","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003071783","display_name":"David F. Anderson","orcid":"https://orcid.org/0000-0002-2344-614X"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"DAVID F. ANDERSON","raw_affiliation_strings":["University of Tennessee, Department of Mathematics, Knoxville, TN 37996-1320, USA"],"affiliations":[{"raw_affiliation_string":"University of Tennessee, Department of Mathematics, Knoxville, TN 37996-1320, USA","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006699882","display_name":"Scott T. Chapman","orcid":"https://orcid.org/0000-0003-1205-6899"},"institutions":[{"id":"https://openalex.org/I191429286","display_name":"Sam Houston State University","ror":"https://ror.org/00yh3cz06","country_code":"US","type":"education","lineage":["https://openalex.org/I191429286"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"SCOTT T. CHAPMAN","raw_affiliation_strings":["Sam Houston University, Department of Mathematics and Statistics, Box 2206, Huntsville, TX 77341-2206, USA"],"affiliations":[{"raw_affiliation_string":"Sam Houston University, Department of Mathematics and Statistics, Box 2206, Huntsville, TX 77341-2206, USA","institution_ids":["https://openalex.org/I191429286"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003071783"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":3.4975,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.91975725,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"22","issue":"05","first_page":"1250040","last_page":"1250040"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9998000264167786,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9606000185012817,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9240999817848206,"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/mathematics","display_name":"Mathematics","score":0.8978302478790283},{"id":"https://openalex.org/keywords/integral-domain","display_name":"Integral domain","score":0.81362384557724},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.667303740978241},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6579250693321228},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6326244473457336},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5679382681846619},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5211932063102722},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5202794671058655},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5159645676612854},{"id":"https://openalex.org/keywords/unique-factorization-domain","display_name":"Unique factorization domain","score":0.4663744568824768},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4055333435535431},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3301653265953064},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.25953322649002075},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23175141215324402},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.08898040652275085},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.04456159472465515}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8978302478790283},{"id":"https://openalex.org/C98486379","wikidata":"https://www.wikidata.org/wiki/Q628792","display_name":"Integral domain","level":3,"score":0.81362384557724},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.667303740978241},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6579250693321228},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6326244473457336},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5679382681846619},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5211932063102722},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5202794671058655},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5159645676612854},{"id":"https://openalex.org/C185592164","wikidata":"https://www.wikidata.org/wiki/Q1052579","display_name":"Unique factorization domain","level":3,"score":0.4663744568824768},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4055333435535431},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3301653265953064},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25953322649002075},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23175141215324402},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.08898040652275085},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.04456159472465515},{"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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196712500403","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500403","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W604307686","https://openalex.org/W1415576118","https://openalex.org/W1551345846","https://openalex.org/W1997243263","https://openalex.org/W1998537439","https://openalex.org/W2005325466","https://openalex.org/W2025587837","https://openalex.org/W2036835997","https://openalex.org/W2051482339","https://openalex.org/W2060844765","https://openalex.org/W2080185879","https://openalex.org/W2084109989","https://openalex.org/W2086799127","https://openalex.org/W2086938344","https://openalex.org/W2090552597","https://openalex.org/W2092950213","https://openalex.org/W2095522817","https://openalex.org/W2149198840","https://openalex.org/W2236631918","https://openalex.org/W2573623072","https://openalex.org/W4212806998","https://openalex.org/W6601743874"],"related_works":["https://openalex.org/W2031295477","https://openalex.org/W4389689297","https://openalex.org/W4235835414","https://openalex.org/W2060844765","https://openalex.org/W122992567","https://openalex.org/W2619596770","https://openalex.org/W2036835997","https://openalex.org/W2040543413","https://openalex.org/W2375604274","https://openalex.org/W47973022"],"abstract_inverted_index":{"Let":[0],"D":[1,28,40,64],"be":[2],"an":[3,36,84],"integral":[4,38,90],"domain.":[5],"In":[6,50],"this":[7],"paper,":[8],"we":[9,52],"investigate":[10],"two":[11],"(integer-":[12],"or":[13],"\u221e-valued)":[14],"invariants":[15],"\u03c9(D,":[16,66],"x)":[17,67,75],"and":[18,33,70,76,79,81,92],"\u03c9(D)":[19],"which":[20],"measure":[21],"how":[22,34],"far":[23,35],"a":[24,44,59,93],"nonzero":[25,60,94],"x":[26,62,95],"\u2208":[27,63,96],"is":[29,41,58],"from":[30,42],"being":[31,43],"prime":[32],"atomic":[37],"domain":[39,47],"unique":[45],"factorization":[46],"(UFD),":[48],"respectively.":[49],"particular,":[51],"are":[53],"interested":[54],"in":[55],"when":[56],"there":[57],"(irreducible)":[61],"with":[65],"=":[68],"\u221e":[69],"the":[71],"relationship":[72],"between":[73],"\u03c9(A,":[74],"\u03c9(B,":[77],"x),":[78],"\u03c9(A)":[80],"\u03c9(B),":[82],"for":[83],"extension":[85],"A":[86],"\u2286":[87],"B":[88],"of":[89],"domains":[91],"A.":[97]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
