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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제60권 제1호
- 발행연도
- 2023.1
- 수록면
- 1 - 32 (32page)
- DOI
- 10.4134/JKMS.j210494
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초록· 키워드
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In this paper, we present a method of characterizing minimal polynomials on the ring $\Z_p$ of $p$-adic integers in terms of their coefficients for an arbitrary prime $p$. We first revisit and provide alternative proofs of the known minimality criteria given by Larin \cite{La} for $p=2$ and Durand and Paccaut \cite{DP} for $p=3$, and then we show that for any prime $p\geq 5,$ the proposed method enables us to classify all possible minimal polynomials on $\Zp$ in terms of their coefficients, provided that two prescribed prerequisites for minimality are satisfied.
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