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Volume 34 • Number 2 • 2011
 
• Prime Ideals in Semirings
Vishnu Gupta and J.N. Chaudhari

Abstract.
In this paper, we prove the following theorems:
  1. A nonzero ideal \(I\) of \((\mathbb{Z}^+,+,\cdot)\) is prime if and only if \(I=\langle p\rangle\) for some prime number \(p\) or \(I=\langle 2,3\rangle\).
  2. 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 \(ra=0\}\).

2010 Mathematics Subject Classification: 16Y60.

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