Solvability and number of roots of bi-quadratic equations over p−adic fields

Solvability and number of roots of bi-quadratic equations over p−adic fields

Unlike the real number field R, a bi-quadratic equation x4 + 1 = 0 is solvable over some p−adic number fields Qp, say p = 17, 41, · · · . Therefore, it is of independent interest to provide a solvability criterion for the bi-quadratic equation over p−adic number fields Qp. In this paper, we provide...

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Main Authors: Saburov, Mansoor, Ahmad, Mohd Ali Khameini
Format: Article
Language:English
English
Published: Institute Mathematical Sciences, Universiti Putra Malaysia 2016
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/51131/
http://irep.iium.edu.my/51131/
http://irep.iium.edu.my/51131/1/Bi-Quadratic_Eq_---_MJMS.pdf
http://irep.iium.edu.my/51131/4/51131-Solvability%20and%20number%20of%20roots%20of%20bi-quadratic%20equations%20over%20p-adic%20fields_SCOPUS.pdf
id iium-51131
recordtype eprints
spelling iium-511312017-03-21T11:08:11Z http://irep.iium.edu.my/51131/ Solvability and number of roots of bi-quadratic equations over p−adic fields Saburov, Mansoor Ahmad, Mohd Ali Khameini QA Mathematics Unlike the real number field R, a bi-quadratic equation x4 + 1 = 0 is solvable over some p−adic number fields Qp, say p = 17, 41, · · · . Therefore, it is of independent interest to provide a solvability criterion for the bi-quadratic equation over p−adic number fields Qp. In this paper, we provide solvability criteria for the bi-quadratic equation x4 + ax2 = b over domains Z ∗ p, Zp \ Z ∗ p, Qp \ Zp, Qp, where p > 2. Moreover, we also provide the number of roots of the bi-quadratic equation over the mentioned domains. Institute Mathematical Sciences, Universiti Putra Malaysia 2016-02 Article PeerReviewed application/pdf en http://irep.iium.edu.my/51131/1/Bi-Quadratic_Eq_---_MJMS.pdf application/pdf en http://irep.iium.edu.my/51131/4/51131-Solvability%20and%20number%20of%20roots%20of%20bi-quadratic%20equations%20over%20p-adic%20fields_SCOPUS.pdf Saburov, Mansoor and Ahmad, Mohd Ali Khameini (2016) Solvability and number of roots of bi-quadratic equations over p−adic fields. Malaysian Journal of Mathematical Sciences, 10 (S) (Part 1). pp. 15-35. ISSN 1823-8343 http://einspem.upm.edu.my/journal/fullpaper/vol10sfeb/No2.pdf
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
English
topic QA Mathematics
spellingShingle QA Mathematics
Saburov, Mansoor
Ahmad, Mohd Ali Khameini
Solvability and number of roots of bi-quadratic equations over p−adic fields
description Unlike the real number field R, a bi-quadratic equation x4 + 1 = 0 is solvable over some p−adic number fields Qp, say p = 17, 41, · · · . Therefore, it is of independent interest to provide a solvability criterion for the bi-quadratic equation over p−adic number fields Qp. In this paper, we provide solvability criteria for the bi-quadratic equation x4 + ax2 = b over domains Z ∗ p, Zp \ Z ∗ p, Qp \ Zp, Qp, where p > 2. Moreover, we also provide the number of roots of the bi-quadratic equation over the mentioned domains.
format Article
author Saburov, Mansoor
Ahmad, Mohd Ali Khameini
author_facet Saburov, Mansoor
Ahmad, Mohd Ali Khameini
author_sort Saburov, Mansoor
title Solvability and number of roots of bi-quadratic equations over p−adic fields
title_short Solvability and number of roots of bi-quadratic equations over p−adic fields
title_full Solvability and number of roots of bi-quadratic equations over p−adic fields
title_fullStr Solvability and number of roots of bi-quadratic equations over p−adic fields
title_full_unstemmed Solvability and number of roots of bi-quadratic equations over p−adic fields
title_sort solvability and number of roots of bi-quadratic equations over p−adic fields
publisher Institute Mathematical Sciences, Universiti Putra Malaysia
publishDate 2016
url http://irep.iium.edu.my/51131/
http://irep.iium.edu.my/51131/
http://irep.iium.edu.my/51131/1/Bi-Quadratic_Eq_---_MJMS.pdf
http://irep.iium.edu.my/51131/4/51131-Solvability%20and%20number%20of%20roots%20of%20bi-quadratic%20equations%20over%20p-adic%20fields_SCOPUS.pdf
first_indexed 2023-09-18T21:12:21Z
last_indexed 2023-09-18T21:12:21Z
_version_ 1777411336899133440

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