KARAKTERISASI RING ABEL-GRASSMANN BERDASARKAN SIFAT-SIFAT IDEALNYA

RIKHWANUL LUKMAN, Prof. Dr. Sri Wahyuni, S.U.

2016 | Tesis | S2 Matematika

Pada tesis ini secara umum dibahas tentang ideal, sistem I,M, dan P, himpunansubstraktifdansemisubstraktif, dan ideal prima lemah di ringAbel-Grassmann. Lebih lanjut didefinisikan juga ideal kuasi prima dan kuasi semiprima. Materi terkait ideal di ring Abel-Grassmann digunakan untuk menyelidiki sifat-sifat ideal terkait ring Abel-Grassmann, karakteristik ideal prima dan ideal prima lemah, dan hubungannya dengan sistem I melalui ideal iredusibel. Selanjutnya, diselidiki hubungan antara sistem M dan P di ring Abel-Grassmann dengan ideal kuasi prima dan ideal kuasi semiprima. Terakhir, didefinisikan himpunan substraktif dan himpunan semisubstraktif dan diperoleh hubungan antara ideal kuasi semiprima dan himpunan semisubstraktif.

In this thesis, we discuss about ideals, I,M, and P system, substractive and semi-substractive sets, and weakly prime ideals in Abel-Grassmann ring. Futhermore, quasiprime and quasi-semiprime ideals are also defined. Ideals in Abel-Grassmann ring notions are used to investigate about properties of ideals, prime and weakly prime ideals characterizations, and relations with I system through irreducibel ideal. Next, we investigate relations among M and P-system and quasi-prime and quasi-semiprime in Abel-Grassmann ring. Finally, substractive and semi-substractive sets are also defined and we get result a relation between quasi-semiprime ideal and semi-substractive sets.

Kata Kunci : ring Abel-Grassmann, ideal, ideal kuasiprima, sistem I,M,P, himpunan substraktif, ideal prima lemah.