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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2016.1
- 수록면
- 1,085 - 1,101 (17page)
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In this paper, all rings are commutative with nonzero identity. Let $M$ be an $R$-module. A proper submodule $N$ of $M$ is called a {\it classical prime submodule}, if for each$m\in M$ and elements $a,b\in R$, $abm\in N$ implies that $am\in N$ or $bm\in N$. We introduce theconcept of ``weakly classical prime submodules'' and we will show that this class of submodules enjoys many properties of weakly 2-absorbing ideals of commutative rings. A proper submodule $N$ of $M$ is a {\it weakly classical prime submodule} if whenever $a,b\in R$ and $m\in M$ with $0\neq abm\in N$,then $am\in N$ or $bm\in N$.
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참고문헌 (25)
참고문헌 신청
M. M. Ali / 2008 / Idempotent and nilpotent submodules of multiplication modules / Comm. Algebra 36:4620~4642
R. Ameri / 2003 / On the prime submodules of multiplication modules / Inter. J. Math. Math. Sci. 27:1715~1724
D. F. Anderson / 2011 / On n-absorbing ideals of commutative rings / Comm. Algebra 39:1646~1672
D. D. Anderson / 2003 / Weakly prime ideals / Houston J. Math. 29:831~840
A. Azizi / 2008 / On prime and weakly prime submodules / Vietnam J. Math. 36(3):315~325
R. Ameri / 2003 / On the prime submodules of multiplication modules / Inter. J. Math. Math. Sci. 27:1715~1724
D. F. Anderson / 2011 / On n-absorbing ideals of commutative rings / Comm. Algebra 39:1646~1672
D. D. Anderson / 2003 / Weakly prime ideals / Houston J. Math. 29:831~840
A. Azizi / 2008 / On prime and weakly prime submodules / Vietnam J. Math. 36(3):315~325
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