Karakterisasi Pusat Gelanggang Polinom Miring Atas Matriks Riil 3x3
DOI:
https://doi.org/10.59632/leibniz.v5i02.500Keywords:
Gelanggang Polinom Miring, Pusat, Endomorfisma, Gelanggang MatriksAbstract
Pusat dari gelanggang polinom miring berperan penting dalam memahami sifat simetri dan komutativitas dalam struktur aljabar nonkomutatif. Konsep ini memiliki relevansi dalam pengembangan teori modul dan aplikasi seperti pengkodean dan kriptografi. Dalam penelitian ini, dikarakterisasi pusat dari gelanggang polinom miring atas gelanggang matriks riil 3×3. Hasil ini diperoleh dengan membangun sebuah endomorfisma pada gelanggang matriks riil 3×3, yang kemudian digunakan untuk mengkonstruksi gelanggang polinom miring. Hasil utama menunjukkan bahwa pusat gelanggang tersebut terdiri tepat dari polinomial-polinomial berderajat genap dengan koefisien berupa matriks skalar riil. Struktur ini muncul dari syarat bahwa elemen pusat harus komutatif terhadap operasi dalam gelanggang R dan terhadap x. Pembuktian dilakukan menggunakan argumen inklusi ganda.
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