Avonmantike, Gamalesyone Faria (2018) R-Ideal Pada Semigrup Komutatif. Sarjana thesis, Universitas Brawijaya.
Abstract
Teori ideal pada semigrup komutatif mengalami perkembangan sehingga dihasilkan definisi ideal baru yang disebut -ideal. Annihilator digunakan untuk menentukan elemen regular yang memiliki peran penting dalam konsep ideal ini. Misalkan adalah semigrup komutatif terhadap operasi pergandaan dengan . ideal sejati dari dikatakan -ideal jika dengan , maka untuk setiap . Oleh karena itu, dapat dibuktikan bahwa ideal pokok, ideal prima dan ideal maksimal adalah -ideal serta irisan dan gabungan dari -ideal juga merupakan -ideal.
English Abstract
The ideal theory of commutative semigroups is progressed to form another definition of ideals called -ideal. Annihilator is used to determine the regular elements that have an important role. Let be a commutative multiplicative semigroup with . The proper ideal of is to be -ideal if with , then for every . Therefore, it can be proved that the principal ideal, prime ideal and maximal ideal are -ideal, then union and intersection of -ideal are also -ideal.
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/FMIPIA/2018/28/051800541 |
| Uncontrolled Keywords: | semigrup, ideal, ideal pokok, ideal prima, ideal maksimal, r-ideal, annihilator, semigroup, ideal, principal ideal, prime ideal, maximal ideal, r-ideal, annihilator. |
| Subjects: | 500 Natural sciences and mathematics > 510 Mathematics > 510.1 Philosophy and theory |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Nur Cholis |
| Date Deposited: | 09 Feb 2018 02:34 |
| Last Modified: | 22 Oct 2021 06:37 |
| URI: | http://repository.ub.ac.id/id/eprint/8845 |
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