지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2017.1
- 수록면
- 581 - 600 (20page)
이용수
초록· 키워드
오류제보하기
A classical result of A. Cohn states that, if we express a prime $p$ in base $10$ as $$p=a_n10^n+a_{n-1}10^{n-1}+\cdots +a_110+a_0,$$ then the polynomial $f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots +a_1x+a_0$is irreducible in $\mathbb Z[x]$. This problem was subsequently generalized to any base $b$ by Brillhart, Filaseta, and Odlyzko. We establish this result of A. Cohn in $O_K[x]$, $K$ an imaginary quadratic field such that its ring of integers, $O_K$, is a Euclidean domain. For a Gaussian integer $\beta$ with $|\beta|>1+\sqrt{2}/2,$ we give another representation for any Gaussian integer using a complete residue system modulo $\beta,$ and then establish an irreducibility criterion in $\mathbb Z[i][x]$ by applying this result.
목차
등록된 정보가 없습니다.
참고문헌 (9)
참고문헌 신청
G. Polya / 1976 / Problems and theorems in analysis, Vol. II / Springer-Verlag
J. Brillhart / 1981 / On an irreducibility theorem of A. Cohn / Canad. J. Math. 33 : 1055 ~ 1059
K. Girstmair / 2005 / On an irreducibility criterion of M. Ram Murty / Amer. Math. Monthly 112 : 269 ~ 270
K. H. Rosen / 2000 / Elementary number theory and its applications / Addison-Wesley
M. Filaseta / 1988 / Irreducibility criteria for polynomials with nonnegative coeffcients / Canad. J. Math. 40 : 339 ~ 351
J. Brillhart / 1981 / On an irreducibility theorem of A. Cohn / Canad. J. Math. 33 : 1055 ~ 1059
K. Girstmair / 2005 / On an irreducibility criterion of M. Ram Murty / Amer. Math. Monthly 112 : 269 ~ 270
K. H. Rosen / 2000 / Elementary number theory and its applications / Addison-Wesley
M. Filaseta / 1988 / Irreducibility criteria for polynomials with nonnegative coeffcients / Canad. J. Math. 40 : 339 ~ 351
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
IRREDUCIBILITY OF POLYNOMIALS WITH A LARGE COEFFICIENT
호남수학학술지
2019 .01
-
IRREDUCIBILITY OF GALOIS POLYNOMIALS
호남수학학술지
2018 .01
-
Irreducibility of Hurwitz polynomials over the ring of integers
한국수학논문집
2019 .01
-
On the irreducibility of sum of two reciprocal polynomials
대한수학회보
2016 .01
-
Modified cyclotomic polynomials
대한수학회보
2022 .11
-
A note on representation numbers of quadratic forms modulo prime powers
대한수학회보
2024 .07
-
Quadratic residue codes over $p$-adic integers and their projections to integers modulo $p^e$
한국수학논문집
2015 .01
-
GALOIS POLYNOMIALS
충청수학회지
2019 .01
-
$SR$-additive codes
대한수학회보
2019 .01
-
Some results on integer-valued polynomials over modules
대한수학회보
2020 .01
-
THE ARTINIAN COMPLETE INTERSECTION QUOTIENT AND THE STRONG LEFSCHETZ PROPERTY
충청수학회지
2019 .01
-
Prime-producing polynomials related to class number one problem of number fields
대한수학회보
2023 .03
-
Galois irreducible polynomials
대한수학회논문집
2017 .01
-
Self similar tiles arising from the unitary number systems in Euclidean rings of imaginary quadratic integers
East Asian Mathematical Journal
2015 .01
-
Magnetic curves in $\mathbb{H}^3\times\mathbb{R}$
대한수학회지
2021 .11
-
CLASSIFICATION OF GALOIS POLYNOMIALS
호남수학학술지
2017 .01
-
Number Systems Pertaining to Euclidean Rings of Imaginary Quadratic Integers
East Asian Mathematical Journal
2015 .01
-
Characterization of functions via commutators of bilinear fractional integrals on Morrey spaces
대한수학회보
2016 .01
-
On the Construction of Polynomial $\beta$-algebras over a Field
Kyungpook Mathematical Journal
2017 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0