Discriminant and integral basis of sextic fields defined by x6+ax+b. Issue 10 (3rd October 2022)

• Record Type: Journal Article
• Authors: Kaur, Sumandeep; Khanduja, Sudesh K.
• Is Part Of: Communications in algebra. Volume 50:Issue 10(2022)
• Page Start: 4401
• Page End: 4436
• Publication Date: 2022-10-03
• Subjects: Discriminant -- integral basis -- p-integral basis; 11R04 -- 11R29; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2022.2061984
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let K = Q ( θ ) be an algebraic number field with θ a root of an irreducible trinomial f ( x ) = x 6 + a x + b belonging to Z [ x ] . In this paper, for each prime number p we compute the highest power of p dividing the discriminant of K in terms of the prime powers dividing a, b and discriminant of f ( x ). An explicit p -integral basis of K is also given for each prime p and a method is described to obtain an integral basis of K from these p -integral bases which is illustrated with examples.