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 with identity. An ideal $N$ of $R$ is called $ideal$-$symmetric$ (resp., $ideal$-$reversible$) if $ABC \subseteq N$ implies $ACB \subseteq N$ (resp., $AB \subseteq N$ implies $BA \subseteq N$) for any ideals $A, B, C$ in $R$. A ring $R$ is called $ideal$-$symmetric$ if zero ideal of $R$ is ideal-symmetric. Let $S(R)$ (called the $ideal$-$symmetric$ $radical$ of $R$) be the intersection of all ideal-symmetric ideals of $R$. In this paper, the following are investigated: (1) Some equivalent conditions on an ideal-symmetric ideal of a ring are obtained; (2) Ideal-symmetric property is Morita invariant; (3) For any ring $R$, we have $S(M_{n}(R)) = M_{n}(S(R))$ where $M_{n}(R)$ is the ring of all $n$ by $n$ matrices over $R$; (4) For a quasi-Baer ring $R$, $R$ is semiprime if and only if $R$ is ideal-symmetric if and only if $R$ is ideal-reversible.
목차
등록된 정보가 없습니다.
참고문헌 (12)
참고문헌 신청
C. Hong / 2009 / Ore extensions of quasi-Baer rings / Comm. Algebra 37 (6) : 2030 ~ 2039
D. Anderson / 1999 / Semigroups and rings whose zero products commute / Comm. Algebra 27 (6) : 2847 ~ 2852
G. Birkenmeier / 1999 / Polynomial extensions of Baer and quasi-Baer rings / J. Pure Appl. Algebra 159 : 25 ~ 42
G. Marks / 2002 / Reversible and symmetric rings / J. Pure Appl. Algebra 174 (3) : 311 ~ 318
G. Mason / 1981 / Re exive ideals / Comm. Algebra 9 (17) : 1709 ~ 1724
D. Anderson / 1999 / Semigroups and rings whose zero products commute / Comm. Algebra 27 (6) : 2847 ~ 2852
G. Birkenmeier / 1999 / Polynomial extensions of Baer and quasi-Baer rings / J. Pure Appl. Algebra 159 : 25 ~ 42
G. Marks / 2002 / Reversible and symmetric rings / J. Pure Appl. Algebra 174 (3) : 311 ~ 318
G. Mason / 1981 / Re exive ideals / Comm. Algebra 9 (17) : 1709 ~ 1724
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
On strongly quasi $J$-ideals of commutative rings
대한수학회논문집
2024 .01
-
Note on n-(1,r)-ideals of commutative rings
Proceedings of the Jangjeon Mathematical Society
2024 .04
-
Radical of an ideal and a primary ideal of an $L$-subring
ANNALS OF FUZZY MATHEMATICS AND INFORMATICS
2023 .06
-
On strongly $1$-absorbing primary ideals of commutative rings
대한수학회보
2020 .01
-
Erratum : Rings in which every ideal contained in the set of zero-divisors is a d-ideal
대한수학회논문집
2023 .01
-
Rings in which every ideal contained in the set of zero-divisors is a d-ideal
대한수학회논문집
2022 .01
-
Symmetric property of rings with respect to the Jacobson radical
대한수학회논문집
2019 .01
-
A generalization of symmetric ring property
대한수학회보
2016 .01
-
On graded $J$-ideals over graded rings
대한수학회논문집
2023 .04
-
QUASI AND BI IDEALS IN LEFT ALMOST RINGS
호남수학학술지
2019 .01
-
SYMMETRY OVER CENTERS
호남수학학술지
2015 .01
-
POWERS OF THE AUGMENTATION IDEAL OF A CYCLIC GROUP RING
호남수학학술지
2015 .01
-
ON THE (n, d)th f-IDEALS
대한수학회지
2015 .01
-
N-pure ideals and mid rings
대한수학회보
2022 .09
-
Symmetricity and reversibility from the perspective of nilpotents
대한수학회논문집
2021 .01
-
Reversibility and symmetry over centers
대한수학회지
2019 .01
-
On a special class of matrix rings
대한수학회논문집
2024 .04
-
GENERALIZED QUASI-PRIMARY RINGS
Advanced Studies in Contemporary Mathematics
2018 .01
-
More on the 2-prime ideals of commutative rings
대한수학회보
2020 .01
-
Strongly Prime Ideals and Primal Ideals in Posets
Kyungpook Mathematical Journal
2016 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0