QOMARIAH, NUR (2017) KAJIAN TEORI IDEAL PERLUASAN SUBTRAKTIF PADA SEMIRING TERNARI. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Pembahasan mengenai teori ideal terus berkembang, salah satunya adalah teori ideal pada semiring ternari. Pada tugas akhir ini, dikaji mengenai karakteristik ideal-ideal pada semiring ternari Z_0^-×Z_0^- yaitu ideal utama, Q-ideal, ideal subtraktif, dan ideal perluasan subtraktif. Bentuk-bentuk ideal tersebut memiliki hubungan dengan bentuk-bentuk ideal pada semiring Z_0^+×Z_0^+. Selanjutnya dengan menggunakan keterkaitan antara ideal perluasan subtraktif dengan Q-ideal, maka juga dikaji mengenai ideal perluasan subtraktif terkecil pada semiring ternari. Selain itu, juga dikaji mengenai ideal prima pada semiring ternari terhadap semiring ternari faktor. Jika diberikan I adalah Q-ideal pada semiring ternari S dan P adalah ideal perluasan subtraktif dari I, maka P adalah ideal prima pada S jika dan hanya jika P∕I_((Q⋂P) ) adalah ideal prima pada S∕I_((Q) ).
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Discussion about ideal theory had been developed, such as ideals theory in ternary semiring. This final project discusses the characterization of ideals in ternary semiring Z_0^-×Z_0^- such as principal ideal, Q-ideal, subtractive ideal, and subtractive extension of an ideal in ternary semiring. Characterization of this ideals having relation with characterization of ideals in semiring Z_0^+×Z_0^+ . Further, with the relation between subtractive extension of a Q-ideal in a ternary semiring, smallest subtractive extension of an ideal in ternary semiring is obtained. And also the prime ideal in quotient ternary semiring is obtained. A subtractive extension P of a Q-ideal I in a ternary semiring S is a prime ideal if and only if P∕I_((Q⋂P) ) is a prime ideal in the quotient ternary semiring S∕I_((Q) ).
| Item Type: | Thesis (Undergraduate) |
|---|---|
| Uncontrolled Keywords: | semiring ternari, ideal perluasan subtraktif, semiring ternari faktor, ideal prima. |
| Subjects: | Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA184 Algebra, Linear |
| Divisions: | Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | - NUR QOMARIAH |
| Date Deposited: | 25 Jan 2017 03:01 |
| Last Modified: | 06 Mar 2019 06:41 |
| URI: | http://repository.its.ac.id/id/eprint/2162 |
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