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bibo:abstract "Near-rings are generalizations of rings that need not be abelian and satisfy\r\neither left or right distributivity. The near-ring considered in this study focuses on\r\nright near-rings with an ideal of the near-ring, denoted by P and referred to as an\r\nideal P. This study aims to examine the concept of ideals in near-rings, analyze\r\nthe properties of near-rings based on an ideal P, and investigate the relationships\r\namong these properties and the concept of a P-completely prime near-ring.\r\nThe research method employed in this study is a literature review with a\r\ntheoretical approach, namely by examining relevant definitions, theorems, and results,\r\nand then verifying them through mathematical proofs and concrete examples.\r\nThe properties based on the ideal P include P-center, P-central, P-idempotent,\r\nP-identity, P-regular, and P-permutable.\r\nThe results show that the concept of an ideal in a near-ring is a generalization\r\nof an ideal in a ring, with adjustments to the right distributive property and the\r\ngroup structure, which need not be abelian. Furthermore, the properties based on\r\nideal P generalize fundamental concepts in algebra, namely center, central, idempotent,\r\nidentity, regular, and permutable, and describe the relationships between\r\nelements of a near-ring and ideal P. A relationship between the P-properties and\r\nP-completely prime near-rings is also established. In particular, if a near-ring is\r\nP-completely prime and P-left permutable, then every P-idempotent element outside\r\nP is P-central."^^xsd:string;
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dc:title "HTML Summary of #78687 \n\nP-IDEAL PRIMA LENGKAP PADA NEAR RING\n\n";
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