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Sidang TA Dheva Ufiz ‘Aliyah membahas Teorema Syarat Perlu dan Syarat Cukup Suatu Modul Bersih

oleh | Apr 17, 2023

Nama : Dheva Ufiz ‘Aliyah
NIM : 24010119120005
Judul : Teorema Syarat Perlu dan Syarat Cukup Suatu Modul Bersih

Yang diselenggarakan pada :
Hari/Tanggal : Selasa, 11 April 2023
Jam : 10.00 WIB – selesai
Tempat : Ruang Lab B Gd. F Lt.2 FSM UNDIP

Tim Penguji :
1. Dr. Nikken Prima Puspita, S.Si., M.Sc.
2. Dr. Redemtus Heru Tjahjana, S.Si., M.Si.
3. Dr. Dra. Titi Udjiani S.R.R.M., M.Si.

Skripsi ini membahas mengenai modul bersih yang merupakan perumuman dari ring bersih. Sebuah 𝑅-modul 𝑀 disebut modul bersih jika ring endomorfisma modulnya adalah ring bersih. Pada skripsi ini diperoleh hasil berupa pembuktian teorema syarat perlu dan syarat cukup suatu modul bersih, yaitu suatu 𝑅-modul 𝑀 dikatakan modul bersih dengan syarat untuk setiap 𝑓 ∈ 𝐸𝑛𝑑𝑅 (𝑀) merupakan elemen bersih jika dan hanya jika 𝑅-modul 𝑀 dapat didekomposisikan menjadi 𝑀 = 𝐶⨁𝐷 sedemikian sehingga berlaku 𝑓(𝐴) ⊆ 𝐶, (1 − 𝑓)(𝐵) ⊆ 𝐷 dan 𝑓: 𝐴 → 𝐶, (1 − 𝑓):𝐵 → 𝐷, dengan 𝑓 dan 1 − 𝑓 keduanya merupakan isomorfisma modul.