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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2016.1
- 수록면
- 107 - 120 (14page)
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초록· 키워드
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Let $R$ be a commutative semiring.
The purpose of this note is to investigate the concept of$2$-absorbing (resp., weakly $2$-absorbing) primary idealsgeneralizing of $2$-absorbing (resp., weakly $2$-absorbing) idealsof semirings. A proper ideal $I$ of $R$ said to be a $2$-absorbing(resp., weakly $2$-absorbing) primary ideal if whenever $a,b,c\in R$such that $abc\in I$ (resp., $0\neq abc\in I$), then either $ab\inI$ or $bc\in \sqrt{I}$ or $ac\in \sqrt{I}$. Moreover, when $I$ is a$Q$-ideal and $P$ is a $k$-ideal of $R/I$ with $I\subseteq P$, it isshown that if $P$ is a $2$-absorbing (resp., weakly $2$-absorbing)primary ideal of $R$, then $P/I$ is a $2$-absorbing (resp., weakly$2$-absorbing) primary ideal of $R/I$ and it is also proved that if$I$ and $P/I$ are weakly $2$-absorbing primary ideals, then $P$ is aweakly $2$-absorbing primary ideal of $R$.
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참고문헌 (18)
참고문헌 신청
P. J. Allen / 1969 / A fundamental theorem of homomorphisms for semirings / Proc. Amer . Math . Soc. 21:412~416
Paul J. Allen / 2006 / Ideal Theory in Commutative A-semirings / Kyungpook Mathematical Journal 46(2):261~271
S. E. Atani / 2007 / The ideal theory in quotient of commutative semirings / Glasnik Matem-aticki 42(62):301~308
S. E. Atani / 2005 / On weakly primary ideals / Georgian Math. J. 12(3):423~429
S. E. Atani / 2013 / Ideals in quotient semirings / Chiang Mai J. Sci. 40(1):77~82
Paul J. Allen / 2006 / Ideal Theory in Commutative A-semirings / Kyungpook Mathematical Journal 46(2):261~271
S. E. Atani / 2007 / The ideal theory in quotient of commutative semirings / Glasnik Matem-aticki 42(62):301~308
S. E. Atani / 2005 / On weakly primary ideals / Georgian Math. J. 12(3):423~429
S. E. Atani / 2013 / Ideals in quotient semirings / Chiang Mai J. Sci. 40(1):77~82
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