{"@context":"http://iiif.io/api/presentation/2/context.json","@type":"sc:Manifest","@id":"https://iiif.quartexcollections.com/wesleyan/iiif/34a8ce14-9e3a-4589-a71d-247c1eb75606/manifest","label":"b2021-f5652","metadata":[{"label":"Title","value":"Finiteness of class number"},{"label":"Name(s)","value":["Gao, Haochen (creator)"]},{"label":"Administrative Note","value":"Drupal Node ID: 23981<br>author email: hgao@wesleyan.edu<br>old filename: 1209_358663"},{"label":"Degree","value":["Bachelor of Arts with Departmental Honors"]},{"label":"Description","value":"<p>In number theory, the study of problems about rational integers may lead to the considerations of higher number rings. It is then a natrual idea to generalize the concept of integers in Q to algebraic integers in an algebraic number feild K. The ring of algebraic integers, being the generalization of Z, is denoted by O_K in K. Although similar to the case in Z, every non-unit, non-zero number x in O_K can be factorized into irreducibles, the uniqueness of factorization fails to hold in general. Instead, it holds for ideals of O_K. The study of ideals in O_K leads to the concept of ideal class group. Its order, called class number, is always finit. In this paper, I introduce two different approaches to show the finiteness of class number.</p>"},{"label":"Digital Identifier","value":"b2021-f5652"},{"label":"Digital Object Identifier (DOI)","value":"https://doi.org/10.14418/wes01.1.2392"},{"label":"Digital Origin","value":["born digital"]},{"label":"Discipline","value":["Mathematics"]},{"label":"Date","value":"April 15, 2021"},{"label":"EDTF Date","value":"D:00 M:00 Y:2021"},{"label":"File Format","value":["application/pdf"]},{"label":"Genre","value":["theses"]},{"label":"Group","value":["Theses & Dissertations"]},{"label":"Held By","value":"Wesleyan University Library, Wesleyan University, Middletown, CT, USA"},{"label":"Item Information","value":"<a href=\"https://onesearch.wesleyan.edu/permalink/01CTW_WU/12cbh08/alma9932797616803768\" target=\"_blank\">2021 F5652</a>"},{"label":"Language","value":["English"]},{"label":"Repository","value":["University Archives"]},{"label":"Rights","value":["In Copyright"]},{"label":"Thesis Advisor(s)","value":["Li, Han"]},{"label":"Type","value":["Text"]}],"description":"Finiteness of class 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