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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제58권 제5호
- 발행연도
- 2021.9
- 수록면
- 1,069 - 1,078 (10page)
- DOI
- 10.4134/BKMS.b190868
이용수
초록· 키워드
오류제보하기
Let $R$ be a commutative ring with identity. A proper ideal $I$ of $R$ is called $1$-absorbing primary (\cite{Bad}) if for all nonunit $a,b,c \in R$ such that $abc \in I$, then either $ab \in I$ or $c \in \sqrt{I}$. The concept of $1$-absorbing primary ideals in a polynomial ring, in a PID and in idealization of a module is studied. Moreover, we introduce weakly $1$-absorbing primary ideals which are generalization of weakly prime ideals and $1$-absorbing primary ideals. A proper ideal $I$ of $R$ is called weakly $1$-absorbing primary if for all nonunit $a,b,c \in R$ such that $0\neq abc \in I$, then either $ab \in I$ or $c \in \sqrt{I}$. Some properties of weakly $1$-absorbing primary ideals are investigated. For instance, weakly $1$-absorbing primary ideals in decomposable rings are characterized. Among other things, it is proved that if $I$ is a weakly $1$-absorbing primary ideal of a ring $R$ and $0 \neq I_1I_2I_3 \subseteq I$ for some ideals $I_1, I_2, I_3$ of $R$ such that $I$ is free triple-zero with respect to $I_1I_2I_3$, then $ I_1I_2 \subseteq I$ or $I_3\subseteq I$.
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참고문헌 (13)
참고문헌 신청
D. D. Anderson / 2003 / Weakly prime ideals / Houston J. Math 29(4):831~840
D. D. Anderson / 2009 / Idealization of a Module / Journal of Commutative Algebra 1(1):3~56
Ayman Badawi / 2007 / On 2-absorbing ideals of commutative rings / Bulletin of the Australian Mathematical Society 75(3):417~429
Ayman Badawi / 2020 / On 1-absorbing primary ideals of commutative rings / Journal of Algebra and Its Applications 19(06):2050111
Ayman Badawi / 2014 / On 2-absorbing primary ideals in commutative rings / 대한수학회보 51(4):1163~1173
D. D. Anderson / 2009 / Idealization of a Module / Journal of Commutative Algebra 1(1):3~56
Ayman Badawi / 2007 / On 2-absorbing ideals of commutative rings / Bulletin of the Australian Mathematical Society 75(3):417~429
Ayman Badawi / 2020 / On 1-absorbing primary ideals of commutative rings / Journal of Algebra and Its Applications 19(06):2050111
Ayman Badawi / 2014 / On 2-absorbing primary ideals in commutative rings / 대한수학회보 51(4):1163~1173
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