KARAKTERISASI MODUL PRIMA DAN MODUL HEREDITER ATAS ALJABAR NAKAYAMA
DOI:
https://doi.org/10.25077/jmu.10.4.527-537.2021Abstract
Misalkan K suatu lapangan, A = KE adalah suatu aljabar lintasan yang bersesuaian dengan suatu graf berarah E. Aljabar lintasan A disebut Nakayama jika aljabar bersifat basic dan terhubung dari graf (graf berarah) EA, dimana setiap titik menjadi sumber dan target paling banyak satu panah. Tulisan ini membahas modul prima dan modul herediter atas aljabar Nakayama tertentu. Modul prima atas aljabar Nakayama dari graf tipe An hanyalah modul sederhana. Selanjutnya, untuk aljabar Nakayama dengan graf berbentuk garis, semua modul projektifnya merupakan modul herediter, sedangkan untuk aljabar Nakayama self-injective, semua modul projektifnya bukan modul herediter.
Kata Kunci: Graf, Aljabar Lintasan, Aljabar Nakayama, Modul Prima, Modul Herediter
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