%0 Thesis
%9 Skripsi
%A Ayu Agustin Kufina, NIM.: 22106010039
%B FAKULTAS SAINS DAN TEKNOLOGI
%D 2026
%F digilib:78687
%I UIN SUNAN KALIJAGA YOGYAKARTA
%K Ideal, Near-Ring, Near-Ring Prima Lengkap P, P-Ideal Prima Lengkap
%P 79
%T P-IDEAL PRIMA LENGKAP PADA NEAR RING
%U https://digilib.uin-suka.ac.id/id/eprint/78687/
%X 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.
%Z Prof. Dr. Dra. Hj. Khurul Wardati, M.Si.