Maximal Ideals in Near-Ring

Abstract

We have been studied near-ring with identity and commutative near-ring. We show that:

i)Every proper ideal is contained in a maximal ideal if R is near-ring with identity.

ii)R is a near field if and only if 0 is a maximal ideal.

iii)M is a maximal ideal of R if and only if the quotient near-ring ???? is near field.

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iv)The ideal P is a prime ideal of R if and only if  R is near integral domain.

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v)Every maximal ideal of R is prime ideal.

Keywords: Commutative Near-ring, near-ring with Identity, Maximal Ideals, Near Field, Prime Ideals, Quotient Near ring.