Ideal-Ideal Invertibel pada Semiring

HANA NISRINA PRATIWI, Prof. Dr. Dra. Sri Wahyuni, S.U.,

2024 | Skripsi | MATEMATIKA

Tugas akhir ini mengkaji konsep ideal invertibel dalam konteks ring dan semiring, serta kaitannya dengan struktur aljabar seperti lapangan hasil bagi, ring hasil bagi, dan ring lokal. Dalam semiring, tantangan muncul ketika mempelajari ideal invertibel dan membentuk semiring hasil bagi serta semiring lokal. Karya tulis ini berupaya mengidentifikasi sifat-sifat ideal invertibel di semiring dan menyelidiki kondisi tambahan yang diperlukan agar sifat-sifat tersebut dapat berlaku, seperti pada ring.

This undergraduate thesis examines the concept of invertible ideal in the context of ring and semiring, and its relation to algebraic structures such as quotient fields, quotient rings, and local rings. In semiring, problem arises when studying invertible ideal and forming quotient semiring and local semiring. This undergraduate thesis seeks to identify the properties of invertible ideal in semiring and investigate the additional conditions needed for these properties to hold, as in rings.

Kata Kunci : ring, lapangan hasil bagi, ring hasil bagi, ring lokal, ideal, ideal invertibel, semiring, semiring hasil bagi, semiring lokal