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- W4323255009 abstract "In this paper, we prove that the family of binomials $x_1^{a_1} cdots x_m^{a_m}-y_1^{b_1}cdots y_n^{b_n}$ with $gcd(a_1, ldots, a_m, b_1, ldots, b_n)=1$ is irreducible by identifying the connection between the irreducibility of a binomial in ${mathbb C}[x_1, ldots, x_m, y_1, ldots, y_n]$ and ${mathbb C}(x_2, ldots, x_m, y_1, ldots, y_n)[x_1]$. 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 $U_i$ with integer entries such that $(a_1, ldots, a_m, b_1, ldots, b_n)^T=U_i be_i$ for $iin {1, ldots, m+n}$, where $be_i$ is the standard basis vector." @default.
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- W4323255009 date "2023-07-10" @default.
- W4323255009 modified "2023-09-30" @default.
- W4323255009 title "Irreducibility of Binomials" @default.
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- W4323255009 doi "https://doi.org/10.24330/ieja.1260484" @default.
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