Representation of algebraic integers as sum of units over the real quadratic fields
Other Title(s)
تمثيل الأعداد الجبرية للحقل التربيعي الحقيقي كمجموع لوحدات الحقل الأساسية
Author
Source
Issue
Vol. 16, Issue 3 (sup) (30 Sep. 2019), pp.781-785, 5 p.
Publisher
University of Baghdad College of Science for Women
Publication Date
2019-09-30
Country of Publication
Iraq
No. of Pages
5
Main Subjects
Topics
Abstract EN
In this paper we generalize Jacobsons results by proving that any integer ? in ?(√?),(?>0,? is a square-free integer), belong to??.
All units of ?(√?) are generated by the fundamental unit ??,(?≥0) having the forms ?=?+√?,?≢1(???4) ?=[(2?−1)+√?]2,?≡1(???4) our generalization build on using the conditions ?+1=?±?−1+(1−?), ?=?±?−1+(1−?).
This leads us to classify the real quadratic fields ?√? into the sets ?1,?2,?3… Jacobsons results shows that ?√2,?√5∈?1 and Sliwa confirm that ?√2 and ?√5 are the only real quadratic fields in ?1.
American Psychological Association (APA)
Baddai, Sad Abbud. 2019. Representation of algebraic integers as sum of units over the real quadratic fields. Baghdad Science Journal،Vol. 16, no. 3 (sup), pp.781-785.
https://search.emarefa.net/detail/BIM-899925
Modern Language Association (MLA)
Baddai, Sad Abbud. Representation of algebraic integers as sum of units over the real quadratic fields. Baghdad Science Journal Vol. 16, no. 3 (Supplement) (2019), pp.781-785.
https://search.emarefa.net/detail/BIM-899925
American Medical Association (AMA)
Baddai, Sad Abbud. Representation of algebraic integers as sum of units over the real quadratic fields. Baghdad Science Journal. 2019. Vol. 16, no. 3 (sup), pp.781-785.
https://search.emarefa.net/detail/BIM-899925
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 784
Record ID
BIM-899925