Kyungpook Mathematical Journal

  • 제60권3호
  • /
  • Pages.445-453
  • /
  • 2020
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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𝜙-prime Subsemimodules of Semimodules over Commutative Semirings

  • Fatahi, Fatemeh (Faculty of Mathematical Sciences, Bouali Sina University) ;
  • Safakish, Reza (Faculty of Mathematical Sciences, Bouali Sina University)
  • 투고 : 2016.12.09
  • 심사 : 2019.01.21
  • 발행 : 2020.09.30
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초록

Let R be a commutative semiring with identity and M be a unitary R-semimodule. 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

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