{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19736"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19736","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Some special cases of Chow groups of complete ramified regular local rings","abstract":"In this thesis we study some special cases of Chow groups of a ramified complete regular local ring R of dimension n. We prove that (a) for codimension 3 Gorenstein ideal I, (I) = 0 in $A\\sb{n-3}(R)$ and (b) for a particular class of almost complete intersection prime ideals P of height i, (P) = 0 in $A\\sb{n-i}(R).$ We also study the above problem when the Eisenstein polynomial is of the form $f = p + X\\sbsp{1}{t\\sb1} + X\\sbsp{2}{t\\sb2} + X\\sbsp{3}{t\\sb3} + X\\sbsp{4}{2} + X\\sbsp{5}{2}$ and $f = p + X\\sbsp{1}{2} + \\cdots + X\\sbsp{n-2}{2} + X\\sbsp{n-1}{4} + X\\sbsp{n}{4}.$ Several other cases of the problem are also established.","abstract_html":"In this thesis we study some special cases of Chow groups of a ramified complete regular local ring R of dimension n. We prove that (a) for codimension 3 Gorenstein ideal I, (I) = 0 in $A\\sb{n-3}(R)$ and (b) for a particular class of almost complete intersection prime ideals P of height i, (P) = 0 in $A\\sb{n-i}(R).$ We also study the above problem when the Eisenstein polynomial is of the form $f = p + X\\sbsp{1}{t\\sb1} + X\\sbsp{2}{t\\sb2} + X\\sbsp{3}{t\\sb3} + X\\sbsp{4}{2} + X\\sbsp{5}{2}$ and $f = p + X\\sbsp{1}{2} + \\cdots + X\\sbsp{n-2}{2} + X\\sbsp{n-1}{4} + X\\sbsp{n}{4}.$ Several other cases of the problem are also established.","abstract_has_math":true,"creators":["Lee, Si-Chang"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Griffith, Phillip A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:16:53Z","date_published":"2011-05-07T12:16:53Z","updated_at":"2026-07-22T22:25:14Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1995 Lee, Si-Chang"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624411","(UMI)AAI9624411"],"render_values":[{"text":"AAI9624411","href":null,"code":true},{"text":"(UMI)AAI9624411","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19736","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Griffith, Phillip A."]},{"key":"dc:creator","label":"Author","values":["Lee, Si-Chang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:16:53Z","10000-01-01","1995"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 Lee, Si-Chang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624411","(UMI)AAI9624411","http://hdl.handle.net/2142/19736"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we study some special cases of Chow groups of a ramified complete regular local ring R of dimension n. We prove that (a) for codimension 3 Gorenstein ideal I, (I) = 0 in $A\\sb{n-3}(R)$ and (b) for a particular class of almost complete intersection prime ideals P of height i, (P) = 0 in $A\\sb{n-i}(R).$ We also study the above problem when the Eisenstein polynomial is of the form $f = p + X\\sbsp{1}{t\\sb1} + X\\sbsp{2}{t\\sb2} + X\\sbsp{3}{t\\sb3} + X\\sbsp{4}{2} + X\\sbsp{5}{2}$ and $f = p + X\\sbsp{1}{2} + \\cdots + X\\sbsp{n-2}{2} + X\\sbsp{n-1}{4} + X\\sbsp{n}{4}.$ Several other cases of the problem are also established.","Made available in DSpace on 2011-05-07T12:16:53Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9624411.pdf: 905498 bytes, checksum: a21734acc9b29e339618fbbcc93d950a (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:39:05Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:16:23-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Some special cases of Chow groups of complete ramified regular local rings"]}]}],"canonical_facts":{"dc:contributor":["Griffith, Phillip A."],"dc:creator":["Lee, Si-Chang"],"dc:date":["2011-05-07T12:16:53Z","10000-01-01","1995"],"dc:description":["In this thesis we study some special cases of Chow groups of a ramified complete regular local ring R of dimension n. We prove that (a) for codimension 3 Gorenstein ideal I, (I) = 0 in $A\\sb{n-3}(R)$ and (b) for a particular class of almost complete intersection prime ideals P of height i, (P) = 0 in $A\\sb{n-i}(R).$ We also study the above problem when the Eisenstein polynomial is of the form $f = p + X\\sbsp{1}{t\\sb1} + X\\sbsp{2}{t\\sb2} + X\\sbsp{3}{t\\sb3} + X\\sbsp{4}{2} + X\\sbsp{5}{2}$ and $f = p + X\\sbsp{1}{2} + \\cdots + X\\sbsp{n-2}{2} + X\\sbsp{n-1}{4} + X\\sbsp{n}{4}.$ Several other cases of the problem are also established.","Made available in DSpace on 2011-05-07T12:16:53Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9624411.pdf: 905498 bytes, checksum: a21734acc9b29e339618fbbcc93d950a (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:39:05Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:16:23-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9624411","(UMI)AAI9624411","http://hdl.handle.net/2142/19736"],"dc:language":["eng"],"dc:rights":["Copyright 1995 Lee, Si-Chang"],"dc:subject":["Mathematics"],"dc:title":["Some special cases of Chow groups of complete ramified regular local rings"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:14Z"}