PRIME IDEALS IN RIGHT TERNARY NEAR-RINGS AND RIGHT TERNARY N-GROUPS

Abstract

A Right Ternary Near-Ring (RTNR) is an algebraic system which is a group under binary addition and a ternary semigroup under ternary multiplication satisfying the right distributive law.  In this paper ν-prime ideals where ν ∈ {0, 1, 2, 3} and equiprime ideals of an RTNR are defined and the relationship among them are discussed.  A comparison between ν-primitive ideals and ν-prime ideals where ν ∈ {0, 1, 2} is given.  If N is an RTNR then ν-prime ideals where ν ∈ {0, 1, 2, 3, e, c} in right ternary N-groups are defined and their relationships are studied.  If ∆ is an ideal of a right-lateral ternary N-group Γ, then the interrelationship between the ideal (∆ : Γ) of N and ∆ are obtained.  If ν = 0, 1, 2, 3, c then ν-semiprime ideals in RTNR and right ternary N-groups are also studied.