IDEAL MAKSIMAL DAN IDEAL PRIMA PADA GAMMA NEAR-RING

Amara Novi Safitri, NIM.: 21106010007 (2025) IDEAL MAKSIMAL DAN IDEAL PRIMA PADA GAMMA NEAR-RING. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

Gamma near-ring is a generalization of near-ring and gamma-ring. The structure of a gamma near-ring is an additive group that is not necessarily commutative with the multiplication operation being a triple mapping to a nonempty set that satisfies right distributive and associative properties. A right distributive nearring that satisfies the associative property on triple mappings is a gamma near-ring with gamma being the multiplication operation on the near-ring. The subset of a gamma near-ring is said to be ideal if and only if the subset is ideal on the nearring. The ideal of a near-ring depends on a constant near-ring, which motivates the emergence of a constant gamma near-ring which is related to the ideal of a gamma near-ring. The concept of constant near-ring gamma motivates the emergence of zero symmetric near-ring gamma. The ideal on the gamma near-ring has an analogous definition to the ideal on the near-ring but the multiplication operation is a triple mapping. Consequently, the definitions of maximal ideal and prime ideal on gamma near-ring are defined similarly to maximal ideal and prime ideal on nearring. The relationship between maximal ideals and prime ideals in rings also holds when viewed as a gamma near-ring. Every maximal ideal of a gamma near-ring with unit element is a prime ideal.

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