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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2020.1
- 수록면
- 445 - 453 (9page)
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Let R be a commutative semiring with identity and M be a unitary Rsemimodule.Let φ : S(M) →S(M) ∪ {?} be a function, where S(M) is the set of all subsemimodules of M. A proper subsemimodule N of M is called φ-prime subsemimodule, if r ∈ R and x ∈ M with rx ∈ N ＼φ(N) implies that r ∈ (N :R M) or x ∈ N. So if we take φ(N) = ? (resp., φ(N) = {0}), a φ-prime subsemimodule is prime (resp., weakly prime). In this article we study the properties of several generalizations of prime subsemimodules.
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참고문헌 (16)
참고문헌 신청
Ahmad Yousefian Darani / 2012 / On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings / Kyungpook Mathematical Journal 52(1):91~97
D. D. Anderson / 2003 / Weakly prime ideals / Houston J. Math 29:831~840
D. D. Anderson / 2008 / Generalizatins of prime ideals / Comm. Algebra 36:686~696
Fatemeh Soheilnia / 2016 / On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative Semiring / Kyungpook Mathematical Journal 56(1):107~120
G. Yesilotr / 2010 / On prime subsemimodules of semimodules / Int. J. Algebra 4(1):53~60
D. D. Anderson / 2003 / Weakly prime ideals / Houston J. Math 29:831~840
D. D. Anderson / 2008 / Generalizatins of prime ideals / Comm. Algebra 36:686~696
Fatemeh Soheilnia / 2016 / On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative Semiring / Kyungpook Mathematical Journal 56(1):107~120
G. Yesilotr / 2010 / On prime subsemimodules of semimodules / Int. J. Algebra 4(1):53~60
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