@phdthesis{digilib78687,
           month = {August},
           title = {P-IDEAL PRIMA LENGKAP PADA NEAR RING},
          school = {UIN SUNAN KALIJAGA YOGYAKARTA},
          author = {NIM.: 22106010039 Ayu Agustin Kufina},
            year = {2026},
            note = {Prof. Dr. Dra. Hj. Khurul Wardati, M.Si.},
        keywords = {Ideal, Near-Ring, Near-Ring Prima Lengkap P, P-Ideal Prima Lengkap},
             url = {https://digilib.uin-suka.ac.id/id/eprint/78687/},
        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.}
}