논문KCI 등재
1-(2-) Prime Ideals in Semirings
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초록
In this paper, we introduce the concepts of 1-prime ideals and 2-prime ideals in semirings. We have also introduced m1-system and m2-system in semiring. We have shown that if Q is an ideal in the semiring R and if M is an m2-system of R such that Q∩M =emptyset then there exists as 2-prime ideal P of R such that Q ⊆ P with P∩M =emptyset.
Abstract
In this paper, we introduce the concepts of 1-prime ideals and 2-prime ideals in semirings. We have also introduced m1-system and m2-system in semiring. We have shown that if Q is an ideal in the semiring R and if M is an m2-system of R such that Q∩M =emptyset then there exists as 2-prime ideal P of R such that Q ⊆ P with P∩M =emptyset.
참고문헌 (6)
- J. Ahsan, "Fully idempotent semirings", Proc. japan Acad., 69, pp.185~188 (1993)
- F.E.Alarcon, "Fully Prime Semirings", Kyungpook Math. J., 40, pp.239~245 (2000)
- P. Dheena, "On regular semirings", Indian Journal of Mathematics, 45(2), pp.135~140 (2003)
- N. H. McCoy, "Theory of Rings" (1964), Macmillan
- M.K.Sen, "On maximal k-ideals of semirings", Proc.Amer. Math.Soc., 118(3), pp.699~703 (1993)
- M.K.Sen, "Von Neumannian Regularity in Semirings", Kyung- pook Math.J., 35, pp.249~258 (1995)
관련 논문AI추천
On 2-absorbing Primary Ideals of Commutative SemigroupBiswaranjan Khanra, Manasi Mandal경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2022 · 제62권 제3호φ-prime Subsemimodules of Semimodules over Commutative SemiringsFatemeh Fatahi, Reza Safakish경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제3호On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative SemiringFatemeh Soheilnia경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제1호On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative SemiringsAhmad Yousefian Darani경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2012 · 제52권 제1호On weakly completely quasi primary and completely quasi primary ideals in ternary semiringsPairote Yiarayong대한수학회 · 대한수학회논문집2016 · 제31권 제4호Weakly prime left ideals in near-subtraction semigroupsG. Satheesh Kumar, P. Dheena대한수학회 · 대한수학회논문집2008 · 제23권 제3호
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