Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields
In this paper we generalize Jacobsons results by proving that any integer in is a square-free integer), belong to . All units of are generated by the fundamental unit having the forms our generalization build on using the conditions This leads us to classify the real quadratic fields int...
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| Language: | English |
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University of Baghdad, College of Science for Women
2019-09-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4152 |
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| author | Saad A. Baddai |
| author_facet | Saad A. Baddai |
| author_sort | Saad A. Baddai |
| collection | DOAJ |
| description | In this paper we generalize Jacobsons results by proving that any integer in is a square-free integer), belong to . All units of are generated by the fundamental unit having the forms
our generalization build on using the conditions
This leads us to classify the real quadratic fields into the sets Jacobsons results shows that and Sliwa confirm that and are the only real quadratic fields in . |
| format | Article |
| id | doaj-art-1ea9aabf9b2f4fc996f5e7ecc09ac82d |
| institution | DOAJ |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2019-09-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-1ea9aabf9b2f4fc996f5e7ecc09ac82d2025-08-20T03:15:47ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862019-09-01163(Suppl.)10.21123/bsj.2019.16.3(Suppl.).0781Representation of Algebraic Integers as Sum of Units over the Real Quadratic FieldsSaad A. BaddaiIn this paper we generalize Jacobsons results by proving that any integer in is a square-free integer), belong to . All units of are generated by the fundamental unit having the forms our generalization build on using the conditions This leads us to classify the real quadratic fields into the sets Jacobsons results shows that and Sliwa confirm that and are the only real quadratic fields in .http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4152Fundamental units of real quadratic field, Integers of real quadratic field as sum of finite units, Real quadratic fields. |
| spellingShingle | Saad A. Baddai Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields مجلة بغداد للعلوم Fundamental units of real quadratic field, Integers of real quadratic field as sum of finite units, Real quadratic fields. |
| title | Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields |
| title_full | Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields |
| title_fullStr | Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields |
| title_full_unstemmed | Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields |
| title_short | Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields |
| title_sort | representation of algebraic integers as sum of units over the real quadratic fields |
| topic | Fundamental units of real quadratic field, Integers of real quadratic field as sum of finite units, Real quadratic fields. |
| url | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4152 |
| work_keys_str_mv | AT saadabaddai representationofalgebraicintegersassumofunitsovertherealquadraticfields |