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.
초록· 키워드
오류제보하기
Let $R$ be an integral domain. We prove that the power series ring $R[\![X]\!]$ is a Krull domain if and only if $R[\![X]\!]$ is a generalized Krull domain and $t$-$\dim R \leq 1$, which improves a well-known result of Paran and Temkin. As a consequence we show that one of the following statements holds: (1) the concepts ``Krull domain" and ``generalized Krull domain" are the same in power series rings, (2) there exists a non-$t$-SFT domain $R$ with $t$-$\dim R > 1$ such that $t$-$\dim R[\![X]\!] =1$.
목차
등록된 정보가 없습니다.
참고문헌 (18)
참고문헌 신청
J. T. Arnold / 1973 / Krull dimension in power series rings / Trans. Amer. Math. Soc. 177:299~304
G. W. Chang / 2015 / The Krull dimension of power series rings over almost Dedekind domains / J. Algebra 438:170~187
G. W. Chang / 2012 / When D((X)) and D{{X}} are Prufer domains / J. Pure Appl. Algebra 216(2):276~279
M. D. Fried / 2008 / Field Arithmetic, third edition, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics / Springer-Verlag :11
R. Gilmer / 1969 / Power series rings over a Krull domain / Pacific J. Math. 29:543~549
G. W. Chang / 2015 / The Krull dimension of power series rings over almost Dedekind domains / J. Algebra 438:170~187
G. W. Chang / 2012 / When D((X)) and D{{X}} are Prufer domains / J. Pure Appl. Algebra 216(2):276~279
M. D. Fried / 2008 / Field Arithmetic, third edition, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics / Springer-Verlag :11
R. Gilmer / 1969 / Power series rings over a Krull domain / Pacific J. Math. 29:543~549
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
Prime Factorization of ideals in commutative rings, with a focus on Krull rings
대한수학회지
2023 .03
-
On $\phi$-pseudo-Krull rings
대한수학회논문집
2020 .01
-
Every abelian group is the class group of a ring of Krull type
대한수학회지
2021 .01
-
On $n$-absorbing ideals and the $n$-Krull dimension of a commutative ring
대한수학회지
2016 .01
-
ON v-MAROT MORI RINGS AND C-RINGS
대한수학회지
2015 .01
-
Power series rings over Pr\"ufer $v$-multiplication domains
대한수학회지
2016 .01
-
A Gorenstein homological characterization of Krull domains
대한수학회보
2024 .05
-
GENERALIZED QUASI-PRIMARY RINGS
Advanced Studies in Contemporary Mathematics
2018 .01
-
Zero divisor graphs of skew generalized power series rings
대한수학회논문집
2015 .01
-
Regularity relative to a hereditary torsion theory for modules over a commutative ring
대한수학회지
2022 .07
-
UN rings and group rings
대한수학회보
2023 .01
-
Archimedean skew generalized power series rings
대한수학회논문집
2019 .01
-
On U-group Rings
대한수학회논문집
2018 .01
-
Some curiosities of the algebra of bounded Dirichlet series
대한수학회보
2016 .01
-
Annihilating content in polynomial and power series rings
대한수학회지
2019 .01
-
On weakly local rings
한국수학논문집
2020 .01
-
N-pure ideals and mid rings
대한수학회보
2022 .09
-
Structures Related to Right Duo Factor Rings
Kyungpook Mathematical Journal
2021 .01
-
A Note on Gaussian Series Rings
Kyungpook Mathematical Journal
2017 .01
-
On the structure of zero-divisor elements in a near-ring of skew formal power series
대한수학회논문집
2021 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0