PRIME IDEALS IN RIGHT TERNARY NEAR-RINGS AND RIGHT TERNARY N-GROUPS - Maheswari, A. Uma; Meera, C. (Italian Journal of Pure and Applied Mathematics, 2015)
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.