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.
이용수
초록· 키워드
오류제보하기
Let $R$ be a ring in which $Nil(R)$ is a divided prime ideal of $R$. Then, for a suitable property $X$ of integral domains, we can define a $\phi$-$X$-ring if $R/Nil(R)$ is an $X$-domain. This device was introduced by Badawi \cite{Ayman1} to study rings with zero divisors with a homomorphic image a particular type of domain. We use it to introduce and study a number of concepts such as $\phi$-Schreier rings, $\phi$-quasi-Schreier rings, $\phi$-almost-rings, $\phi$-almost-quasi-Schreier rings, $\phi$-$GCD$ rings, $\phi$-generalized $GCD$ rings and $\phi$-almost $GCD$ rings as rings $R$ with $Nil(R)$ a divided prime ideal of $R$ such that $R/Nil(R)$ is a Schreier domain, quasi-Schreier domain, almost domain, almost-quasi-Schreier domain, $GCD$ domain, generalized $GCD$ domain and almost $GCD$ domain, respectively. We study some generalizations of these concepts, in light of generalizations of these concepts in the domain case, as well. Here a domain $D$ is pre-Schreier if for all $x, y, z\in D\backslash 0,$ $x\mid yz$ in $D$ implies that $x=rs$ where $r\mid y$ and $s\mid z$. An integrally closed pre-Schreier domain was initially called a Schreier domain by Cohn in \cite{Cohn} where it was shown that a GCD domain is a Schreier domain.
목차
등록된 정보가 없습니다.
참고문헌 (24)
참고문헌 신청
Z. Ahmad / 2013 / Almost quasi Schreier domains / Comm. Algebra 41(5):1685~1696
M. M. Ali / 2001 / Generalized GCD rings / Beitr¨age Algebra Geom 42(1):219~233
D. D. Anderson / 1978 / π-domains divisorial ideals and overrings / Glasgow Math. J 19(1):199~203
D. D. Anderson / 1979 / Generalized GCD domains / Comment. Math. St. Univ. Pauli 28:215~221
D. F. Anderson / 2004 / On φ-Pr¨ufer rings and φ-Bezout rings / Houston J. Math 2(2):331~343
M. M. Ali / 2001 / Generalized GCD rings / Beitr¨age Algebra Geom 42(1):219~233
D. D. Anderson / 1978 / π-domains divisorial ideals and overrings / Glasgow Math. J 19(1):199~203
D. D. Anderson / 1979 / Generalized GCD domains / Comment. Math. St. Univ. Pauli 28:215~221
D. F. Anderson / 2004 / On φ-Pr¨ufer rings and φ-Bezout rings / Houston J. Math 2(2):331~343
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
Average of class numbers of some family of Artin-Schreier extensions of rational function fields
한국수학논문집
2016 .01
-
On $\phi$-sharp rings
대한수학회논문집
2016 .01
-
On $\phi$-$(n,d)$ rings and $\phi$-$n$-coherent rings
대한수학회논문집
2024 .07
-
A generalization of the prime radical of ideals in commutative rings
대한수학회논문집
2017 .07
-
On $\phi$-$w$-flat modules and their homological dimensions
대한수학회보
2021 .01
-
A generalization of $w$-linked extensions
대한수학회보
2022 .05
-
AVERAGE OF L-FUNCTIONS OF ARTIN-SCHREIER EXTENSIONS
충청수학회지
2016 .01
-
A question about maximal non $\phi$-chained subrings
대한수학회논문집
2023 .01
-
On artinianness of general local cohomology modules
대한수학회보
2021 .01
-
Order, type and zeros of analytic and meromorphic functions of $\left[p,q\right]-\phi$ order in the unit disc
한국수학논문집
2023 .06
-
A note on $\phi$-Pr\"{u}fer $v$-multiplication rings
대한수학회보
2022 .09
-
A variant of d'Alembert's and Wilson's functional equations for matrix valued functions
대한수학회논문집
2024 .07
-
On $\phi$-pseudo-Krull rings
대한수학회논문집
2020 .01
-
On $\phi$-$n$-absorbing primary ideals of commutative rings
대한수학회지
2016 .01
-
Global Histidine Phosphoproteomics in Human Prostate Cancer Cells
Mass Spectrometry Letters
2020 .09
-
EXISTENCE OF THE SOLUTION OF COUNTABLY INFINITE SYSTEM OF DIFFERENTIAL EQUATIONS IN SEQUENCE SPACES m<sup>p</sup>(𝜙) AND n<sup>p</sup>(𝜙) WITH THE HELP OF MEASURE OF NON-COMPACTNESS
Journal of applied mathematics & informatics
2019 .01
-
Nonnil-P-coherent rings and nonnil-PP-rings
대한수학회보
2024 .09
-
HAUSDORFF DIMENSION OF THE SET CONCERNING WITH BOREL-BERNSTEIN THEORY IN L¨UROTH EXPANSIONS
대한수학회지
2017 .07
-
UN rings and group rings
대한수학회보
2023 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0