Open AccessMODUL FAKTOR YANG DIBENTUK DARI SUBMODUL Z^2 PADA MODUL R^2 ATAS GAUSSIAN INTEGERS
Author(s) -
Ari Wardayani
Publication year - 2012
Publication title -
jurnal ilmiah matematika dan pendidikan matematika (jmp)/jurnal ilmiah matematika dan pendidikan matematika
Language(s) - English
Resource type - Journals
eISSN - 2550-0422
pISSN - 2085-1456
DOI - 10.20884/1.jmp.2012.4.2.2964
Subject(s) - mathematics , coset , gaussian , gaussian integer , quotient , set (abstract data type) , discrete mathematics , eisenstein integer , combinatorics , computer science , algebraic number , mathematical analysis , physics , quantum mechanics , programming language
We prove that ℝ2 is module over Gaussian Intergers and the set of all coset of submodule in module ℝ2 over Gaussian Integers is a quotient module. We find the proof by showing that ℝ2 is both a right module and a left module over Gaussian Integers and showing that the set of all coset of submodule in module ℝ2 is both a right module and a left module over Gaussian Integers.