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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| Format: | Article |
| Language: | Arabic |
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College of Science for Women, University of Baghdad
2019-09-01
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| Series: | Baghdad Science Journal |
| Subjects: | |
| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4152 |
| _version_ | 1828496642949513216 |
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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 . |
| first_indexed | 2024-12-11T12:33:21Z |
| format | Article |
| id | doaj.art-1ea9aabf9b2f4fc996f5e7ecc09ac82d |
| institution | Directory Open Access Journal |
| issn | 2078-8665 2411-7986 |
| language | Arabic |
| last_indexed | 2024-12-11T12:33:21Z |
| publishDate | 2019-09-01 |
| publisher | College of Science for Women, University of Baghdad |
| record_format | Article |
| series | Baghdad Science Journal |
| spelling | doaj.art-1ea9aabf9b2f4fc996f5e7ecc09ac82d2022-12-22T01:07:11ZaraCollege of Science for Women, University of BaghdadBaghdad Science Journal2078-86652411-79862019-09-01163(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 Baghdad Science Journal 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 |