P-IDEAL PRIMA LENGKAP PADA NEAR RING

Ayu Agustin Kufina, NIM.: 22106010039 (2026) P-IDEAL PRIMA LENGKAP PADA NEAR RING. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

Near-rings are generalizations of rings that need not be abelian and satisfy either left or right distributivity. The near-ring considered in this study focuses on right near-rings with an ideal of the near-ring, denoted by P and referred to as an ideal P. This study aims to examine the concept of ideals in near-rings, analyze the properties of near-rings based on an ideal P, and investigate the relationships among these properties and the concept of a P-completely prime near-ring. The research method employed in this study is a literature review with a theoretical approach, namely by examining relevant definitions, theorems, and results, and then verifying them through mathematical proofs and concrete examples. The properties based on the ideal P include P-center, P-central, P-idempotent, P-identity, P-regular, and P-permutable. The results show that the concept of an ideal in a near-ring is a generalization of an ideal in a ring, with adjustments to the right distributive property and the group structure, which need not be abelian. Furthermore, the properties based on ideal P generalize fundamental concepts in algebra, namely center, central, idempotent, identity, regular, and permutable, and describe the relationships between elements of a near-ring and ideal P. A relationship between the P-properties and P-completely prime near-rings is also established. In particular, if a near-ring is P-completely prime and P-left permutable, then every P-idempotent element outside P is P-central.

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