φ-prime Subsemimodules of Semimodules over Commutative Semirings

다국어 초록 (Multilingual Abstract)

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.

참고문헌 (Reference)

1 N. Zamani, "φ-prime submodules" 52 (52): 253-259, 2010

2 R. Safakish, "φ-primary subtractive ideals in semirings" 108 (108): 629-633, 2016

3 J. N. Chaudhari, "Weakly prime subsemimodules of semimodules over semirings" 5 (5): 167-174, 2011

4 D. D. Anderson, "Weakly prime ideals" 29 : 831-840, 2003

5 R. Ebrahimi Atani, "Spectra of semimodule" 3 (3): 15-28, 2011

6 J. S. Golan, "Semiring and their Applications" Kluwer Academic publisher 1999

7 M. Bataineh, "Primal and weakly primal subsemimodules" 4 (4): 131-135, 2014

8 G. Yesilotr, "On prime subsemimodules of semimodules" 4 (4): 53-60, 2010

9 R. P. Deore, "On associated primes and primary subsemimodule" 2 (2): 795-801, 2008

10 Jaiprakash Ninu Chaudhari, "On Partitioning and Subtractive Subsemimodules of Semi- modules over Semirings" 경북대학교 자연과학대학 수학과 50 (50): 329-336, 2010

11 Fatemeh Soheilnia, "On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative Semiring" 경북대학교 자연과학대학 수학과 56 (56): 107-120, 2016

12 Ahmad Yousefian Darani, "On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings" 경북대학교 자연과학대학 수학과 52 (52): 91-97, 2012

13 D. D. Anderson, "Generalizatins of prime ideals" 36 : 686-696, 2008

14 V. Gupta, "Characterisation of weakly prime subtractive ideals in semirings" 3 : 347-352, 2008

15 S. Ebrahimi Atani, "A note on finitely generated multiplication semimodules over commutative semirings" 4 (4): 389-396, 2010

16 S. Ebrahimi Atani, "A Zariski topology for semimodules" 4 (4): 251-265, 2011