KOLEKSI MODUL KO-BEBAS LINEAR DAN GENERALISASI RANK MODUL

WILLY SUMARNO, Dr.rer.nat. Indah Emilia Wijayanti, M.Si.; Dr. Budi Surodjo, M.Si.

2018 | Skripsi | S1 MATEMATIKA

Koleksi modul ko-bebas linear merupakan dual koleksi modul bebas linear. Koleksi R-modul U dikatakan ko-bebas linear terhadap M jika terdapat R-epimorfisma modul dari M ke hasil kali anggota-anggota U. Sifat-sifat koleksi modul ko-bebas linear merupakan dual sifat-sifat koleksi modul bebas linear juga. Lebih lanjut, rank modul dapat diperumum dengan bantuan definisi dan sifat-sifat koleksi modul pembangun, koleksi modul ko-pembangun, koleksi modul bebas linear, dan koleksi modul ko-bebas linear. Sifat batas atas dan batas bawah generalisasi rank modul dapat dikaitkan dengan sifat modul Artin dan modul Noether.

Co-linearly independent collection of modules is a dual of linearly independent collection of modules. A collection U of R-modules is said to be co-linearly independent to M if there is an R-module epimorphism from M to the product of elements of U. The properties of co-linearly independent collection of modules are also dual of the properties of linearly independent collection of modules. Moreover, the rank of modules can be generalized with the help of the definitions and the properties of generating collection of modules, co-generating collection of modules, linearly independent collection of modules, and co-linearly independent collection of modules. The properties of the upper bounds and the lower bounds of generalized rank of modules can be connected with the properties of Artinian modules and Noetherian modules.

Kata Kunci : Modul ko-bebas linear, Generalisasi rank modul