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- W3121569256 abstract "We discuss principality of prime ideals of finite algebraic number fields $L=K(theta)$ over an algebraic number field $K ([K:mathbb{Q}]<infty)$ defined by irreducible polynomials $f(x)in mathfrak{O}_{K}[x]$ and $f(theta)=0$. Our main Theorem says that if a principal prime ideal $(pi)subset mathfrak{O}_{K}$ is relatively prime to conductor $mathfrak{F} ={alphain mathfrak{O}_{L}|$ a principal ideal $(alpha)$ of $mathfrak{O}_{L}subset mathfrak{O}_{K}[theta]}$ and splits completely over $L$: $(pi)mathfrak{O}_{L}=prod mathfrak{p}_{i}$, then $mathfrak{p}_{i}$ is a principal ideal of $mathfrak{O}_{L}$ for all $i$, where $mathfrak{O}_{L}= L cap overline{mathbb{Z}}$ is integer ring of $L$. We use Jacobian Varieties of non-singular projective curve model of super elliptic curves $y^{l}=f(x)$ to show the main Theorem, where $l$ is a large enough prime number which is relatively prime to degree of $f(x)$ and $(pi)$." @default.
- W3121569256 created "2021-02-01" @default.
- W3121569256 creator A5085887673 @default.
- W3121569256 date "2021-01-25" @default.
- W3121569256 modified "2023-09-27" @default.
- W3121569256 title "Principality of prime ideals of algebraic number fields" @default.
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