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
In \cite{Hamed1}, the authors generalize the concept of the class group of an integral domain $D$ ($Cl_t(D)$) by introducing the notion of the $S$-class group of an integral domain where $S$ is a multiplicative subset of $D.$ The $S$-class group of $D,$ $S$-$Cl_t(D),$ is the group of fractional $t$-invertible $t$-ideals of $D$ under the $t$-multiplication modulo its subgroup of $S$-principal $t$-invertible $t$-ideals of $D.$ In this paper we study when $S$-$Cl_t(D)$ $\simeq$ $S$-$Cl_t(D_T),$ where $T$ is a multiplicative subset generated by prime elements of $D.$ We show that if $D$ is a Mori domain, $T$ a multiplicative subset generated by prime elements of $D$ and $S$ a multiplicative subset of $D,$ then the natural homomorphism $S$-$Cl_t(D) \rightarrow S$-$Cl_t(D_T)$ is an isomorphism. In particular, we give an $S$-version of Nagata's Theorem \cite{Nagata}: Let $D$ be a Krull domain, $T$ a multiplicative subset generated by prime elements of $D$ and $S$ another multiplicative subset of $D.$ If $D_T$ is an $S$-factorial domain, then $D$ is an $S$-factorial domain.
목차
등록된 정보가 없습니다.
참고문헌 (14)
참고문헌 신청
H. Ahmed / 2017 / On the class group and S-class group of formal power series rings / J. Pure Appl. Algebra 221(11):2869~2879
D. D. Anderson / 1988 / Some remarks on star operations and the class group / J. Pure Appl. Algebra 51(1-2):27~33
D. D. Anderson / 2002 / S-Noetherian rings / Comm. Algebra 30(9):4407~4416
D. D. Anderson / 1998 / Anti-Archimedean rings and power series rings / Comm. Algebra 26(10):3223~3238
A. Bouvier / 1982 / Le groupe des classes d'un anneau integre, 107eme Congres des Societes Savantes / Brest :85~92
D. D. Anderson / 1988 / Some remarks on star operations and the class group / J. Pure Appl. Algebra 51(1-2):27~33
D. D. Anderson / 2002 / S-Noetherian rings / Comm. Algebra 30(9):4407~4416
D. D. Anderson / 1998 / Anti-Archimedean rings and power series rings / Comm. Algebra 26(10):3223~3238
A. Bouvier / 1982 / Le groupe des classes d'un anneau integre, 107eme Congres des Societes Savantes / Brest :85~92
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
The Cohen Type Theorem for $S$-$*_w$-Principal Ideal Domains
East Asian Mathematical Journal
2018 .01
-
Prime Factorization of ideals in commutative rings, with a focus on Krull rings
대한수학회지
2023 .03
-
KAPLANSKY-TYPE THEOREMS IN GRADED INTEGRAL DOMAINS
대한수학회보
2015 .01
-
When the Nagata ring ${D(X)}$ is a sharp domain
한국수학논문집
2016 .01
-
A non-Newtonian approach in differential geometry of curves: multiplicative rectifying curves
대한수학회보
2024 .05
-
Automatic continuity of almost multiplicative linear functionals on Fr\'echet algebras
대한수학회보
2016 .01
-
Algebraic entropies of natural numbers with one or two prime factors
순수 및 응용수학
2016 .01
-
Power series rings over Pr\"ufer $v$-multiplication domains
대한수학회지
2016 .01
-
Asymptotic for the number of star operations on one-dimensional Noetherian domains
대한수학회지
2021 .09
-
Every abelian group is the class group of a ring of Krull type
대한수학회지
2021 .01
-
Fractal Analysis and Texture Classification of High-Frequency Multiplicative Noise in SAR Sea-Ice Images Based on a Transform-Domain Image Decomposition Method
극지연구소 초록집
2021 .08
-
ENERGETIC SUBSETS OF BE-ALGEBRAS
호남수학학술지
2017 .01
-
On $n$-absorbing ideals and the $n$-Krull dimension of a commutative ring
대한수학회지
2016 .01
-
Existence of random attractors for stochastic non-autonomous reaction-diffusion equation with multiplicative noise on $\mathbb{R}^{n}$
한국수학논문집
2018 .01
-
ON SOME UNBOUNDED DOMAINS FOR A MAXIMUM PRINCIPLE
순수 및 응용수학
2016 .01
-
A HALF-CENTERED STAR-OPERATION ON AN INTEGRAL DOMAIN
대한수학회지
2017 .01
-
Graded integral domains and Nagata rings, II
한국수학논문집
2017 .06
-
Some remarks on problems of subset sum
대한수학회보
2022 .11
-
A NOTE ON MULTIPLICATIVE (GENERALIZED)-DERIVATION IN SEMIPRIME RINGS
Journal of applied mathematics & informatics
2018 .01
-
A NOTE ON CENTRAL FACTORIAL NUMBERS
Proceedings of the Jangjeon Mathematical Society
2018 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0