Title of article :
Prime Ideals in Semirings
Author/Authors :
Gupta, Vishnu Department of Mathematics - University of Delhi, India , Chaudhari, J.N Department of Mathematics - M. J. College, Jalgaon 425 002, India
Abstract :
In this paper, we prove the following theorems: (1) A nonzero ideal I of (Z^+ ,+, ·) is prime if and only if I = ‹p› for some prime number p or I = ‹2,3›. Let R be a reduced semiring. Then a prime ideal P of R is minimal if and only if P = AP where AP = {r (in) R : (exists) a (notin) P such that ra = 0}.
Keywords :
Semiring , reduced semiring , Bourne factor semiring , subtractive ideal , prime ideal , completely prime ideal , minimal prime ideal
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
