Geodesic
Prime Ideals in Semirings
Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 2 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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In this paper, we prove the following theorems: A nonzero ideal $I$ of $(\mathbb{Z}^+,+,\cdot)$ is prime if and only if $I=\langle p\rangle$ for some prime number $p$ or $I=\langle 2,3\rangle$. Let $R$ be a reduced semiring. Then a prime ideal $P$ of $R$ is minimal if and only if $P=A_P$ where $A_P=\{r\in R:\exists \ a\notin P$ such that $ra=0\}$.
Classification : 16Y60. 
@article{BMMS_2011_34_2_a19,
     author = {Vishnu Gupta and J.N. Chaudhari},
     title = {Prime {Ideals} in {Semirings}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2011},
     volume = {34},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2011_34_2_a19/}
}
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Vishnu Gupta; J.N. Chaudhari. Prime Ideals in Semirings. Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2011_34_2_a19/