Homomorfisma Ring Matriks atas Ring Semigrup

Listiana Listiana, Ahmad Faisol, Fitriani Fitriani

Abstract


Diberikan sebarang ring R dan semigrup S. Ring semigrup R[S] adalah himpunan semua fungsi f dari S ke R dengan supp(f) berhingga yang dilengkapi dengan operasi penjumlahan dan pergandaan yang sama pada ring polinomial R[X]. Di sisi lain, ring matriks M_n (R) adalah himpunan semua matriks atas ring R berukuran n×n yang dilengkapi dengan operasi penjumlahan dan perkalian matriks. Di dalam penelitian ini, dikonstruksi ring matriks M_n (R_1 [S_1 ] ) dan M_n (R_2 [S_2 ] ) dengan R_1,R_2 ring dan S,S_2 semigrup. Selain itu, didefinisikan pemetaan τ dari M_n (R_1 [S_1 ] ) ke M_n (R_2 [S_2 ] ) dengan menggunakan homomorfisma semigrup δ:S_1→S_2 dan homomorfisma ring μ:R_1→R_2. Selanjutnya, dibuktikan τ merupakan homomorfisma ring. Lebih lanjut, diberikan syarat cukup agar τ merupakan monomorfisma.

Keywords


ring semigrup, homomorfisma semigrup, homomorfisma ring, matriks atas ring, ring matriks.

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DOI: http://dx.doi.org/10.12962/limits.v19i2.9790

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