On the clifford algebra of a diagonal binary and cubic form
Author
Source
The Arabian Journal for Science and Engineering. Section A, Science
Issue
Vol. 27, Issue 1A (31 Jan. 2002), pp.109-114, 6 p.
Publisher
King Fahd University of Petroleum and Minerals
Publication Date
2002-01-31
Country of Publication
Saudi Arabia
No. of Pages
6
Main Subjects
Topics
Abstract AR
يعنى هذا البحث, بدراسة جبر كليفور C لشكل مكعب ثنائي قطري f(x,yY) = aX3 + bY3 على حلقة تبادلية A بحيث يكون 6ab عنصر قابل للقلب في A.
نبرهن أولا على أن جبر كليفور C هو جبر أزومايا.
و في حالة K = A جسم ذو مميز يخالف 2 و 3 و توجد d K و {(0,0)} \K2 (x,y) بحيث f(x,y) فإننا نثبت أن جبر كليفور C و مركزه Z متشابهان في زمرة براور Br(Z).
Abstract EN
In this work, we study the Clifford algebra C of a diagonal binary and cubic form f (X, Y) = aX3 + bY3 over a commutative ring A such that 6ab is invertible.
We show that C is an Azumaya algebra.
Also, under some hypotheses, we answer affirmatively the question of Haile [4] by showing that if A = K is a field of characteristic p ∉ {2, 3} and if f is isotropic or represents d3 for some d ∈K – {0}, then the Clifford algebra C is similar to its center Z in Brauer group Br (Z) : [C] = [Z] in Br (Z).
American Psychological Association (APA)
Mahdou, Najib. 2002. On the clifford algebra of a diagonal binary and cubic form. The Arabian Journal for Science and Engineering. Section A, Science،Vol. 27, no. 1A, pp.109-114.
https://search.emarefa.net/detail/BIM-360233
Modern Language Association (MLA)
Mahdou, Najib. On the clifford algebra of a diagonal binary and cubic form. The Arabian Journal for Science and Engineering. Section A, Science Vol. 27, no. 1A (Jan. 2002), pp.109-114.
https://search.emarefa.net/detail/BIM-360233
American Medical Association (AMA)
Mahdou, Najib. On the clifford algebra of a diagonal binary and cubic form. The Arabian Journal for Science and Engineering. Section A, Science. 2002. Vol. 27, no. 1A, pp.109-114.
https://search.emarefa.net/detail/BIM-360233
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 114
Record ID
BIM-360233