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- Title
IRREDUCIBILITY OF BINOMIALS.
- Authors
Haohao Wang; Wojdylo, Jerzy; Oman, Peter
- Abstract
In this paper, we prove that the family of binomials xaι ∙ ∙ ∙ xmm -- y11 ∙ ∙ ∙ ynn with gcd(aι,..., am, 6χ,..., bn) = 1 is irreducible by identifying the connection between the irreducibility of a binomial in C[x1, . . ., xm, y1, . . ., yn] and C(x2, . . ., xm, y1, . . ., yn)[x1]. Then we show that the necessary and sufficient conditions for the irreducibility of this family of binomials is equivalent to the existence of a unimodular matrix Ui with integer entries such that (a1, . . ., am, b1, . . ., bn)T = Uiei for i ∈ {1, . . ., m + n}, where ei is the standard basis vector.
- Subjects
INTEGERS; MATRICES (Mathematics); POLYNOMIALS; BINOMIAL theorem
- Publication
International Electronic Journal of Algebra, 2023, Vol 34, p62
- ISSN
1306-6048
- Publication type
Article
- DOI
10.24330/ieja.1260484