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The n-th cyclotomic polynomial ${\Phi}_n(x)$ is irreducible over $\mathbb{Q}$ and has integer coefficients. The degree of ${\Phi}_n(x)$ is ${\varphi}(n)$, where ${\varphi}(n)$ is the Euler Phi-function. In this paper, we define Semi-Cyclotomic Polynomial $J_n(x)$. $J_n(x)$ is also irreducible over $\mathbb{Q}$ and has integer coefficients. But the degree of $J_n(x)$ is $\frac{{\varphi}(n)}{2}$. Galois Theory will be used to prove the above properties of $J_n(x)$.
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참고문헌 (4)
참고문헌 신청
J. R. Bastida / 1984 / Field Extensions and Galois Thory, Encyclopedia of Mathmatics and Its Application / Addison-Wesley Publishing Company
T. W. Hungerford / 2014 / Abstract Algebra An Introduction / Brooks/Cole, Cengage Learning
S. Lang / 1984 / Algebra / Addison-Wesley Publishing Company
P. Ribenboim / 1972 / Algebraic Numbers / John Wiley and Sons Inc
T. W. Hungerford / 2014 / Abstract Algebra An Introduction / Brooks/Cole, Cengage Learning
S. Lang / 1984 / Algebra / Addison-Wesley Publishing Company
P. Ribenboim / 1972 / Algebraic Numbers / John Wiley and Sons Inc
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