Risnawita
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Modul Herediter Noether dan Prima (HNP) Dari Modul Sederhana Chen A_` Risnawita; Savoji, Fatemeh; Dwi Devi Wulandari
Lattice Journal : Journal of Mathematics Education and Applied Vol. 4 No. 1 (2024): Juni 2024
Publisher : Universitas Islam Negeri Sjech M. Djamil Djambek Bukittinggi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30983/lattice.v4i1.8679

Abstract

Let K be a  field and  is  line graph with infinite path.  Let L is a Leavitt path algebra with correspondence with graph E. Suppose   is a module over ring  (written- module , a module  is considered to be hereditary if all its submodules are projective. A module  is called a Noetherian module if   is a finitely generated module. Suppose M is a left module over the gelanggang  (written - module  ). A proper submodule of  is said to be prime if  with    and  implies  or  . In this  paper we will look at the characteristics of the hereditary nooetherian and prime  modules in the context of Leavitt path algebra.  Let L is a Leavitt path algebra, where E is a line graphs with infinite path and M is a module over Leavitt path algebra L, we find that then M is simple modules which is hereditary noetherian and not prime modules.     Misalkan  adalah suatu lapangan dan merupakan graf garis yang lintasannya tak terhingga. Misalkan  adalah aljabar lintasan Leavitt yang berkorespondensi dengan graf  Misalkan adalah modul di atas gelanggang (ditulis -modul ), modul  dikatakan herediter jika semua submodulnya bersifat proyektif. Modul M disebut modul Noetherian jika  adalah modul yang dibangun secara hingga. Misalkan adalah modul kiri atas gelanggang  (ditulis -modul ). Suatu submodul sejati dari  dikatakan prima jika  dengan  dan  mengakibatkan  atau . Dalam tulisan ini kita akan melihat karakteristik modul herediter noether dan prima dalam konteks aljabar lintasan Leavitt.  Misalkan adalah aljabar lintasan Leavitt, dengan  adalah graf garis yang memuat lintasan tak berhingga. Dan  adalah modul atas aljabar lintasan Leavitt  kita temukan bahwa M adalah modul sederhana yang merupakan modul herediter Noether dan bukan modul prima.
Pengaruh Model Pembelajaran MURDER terhadap Kemampuan Pemahaman Konsep Matematis Siswa Fitria, Atsari; Rahmat, Tasnim; M. Imamuddin; Risnawita
Indo-MathEdu Intellectuals Journal Vol. 6 No. 7 (2025): Indo-MathEdu Intellectuals Journal
Publisher : Lembaga Intelektual Muda (LIM) Maluku

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.54373/imeij.v6i7.4518

Abstract

The problem in this study is the low ability to understand mathematical concepts in students. Furthermore, the learning process carried out by teachers uses conventional learning, resulting in a lack of student activeness during the learning process. This study aims to determine whether there is an effect of the MURDER learning model on students' understanding of mathematical concepts. This type of research is quantitative. The research method used is an experimental research method with a Posttest Only Group Design. The research population is grade X Phase E students at SMA N 1 Lembah Melintang. Sampling was carried out using a simple random sampling technique. The sample in this study was students from class XE2 as the experimental class, totaling 33 people, and class XE4 as the control class, totaling 33 people. The research instrument used was a test of students' mathematical concept understanding abilities. The data analysis technique using the t-test obtained t_hitung=5,08 and t_tabel=1,67. While using Minitab Software obtained P_Value=0,000. Because t_hitung>t_tabel and P_Value<α with a significance level of α=0,05, H_0 is rejected. The results of the study are "There is an influence of the MURDER learning model on students' understanding of mathematical concepts." The problem in this study is the low ability to understand mathematical concepts in students. Furthermore, the learning process carried out by teachers uses conventional learning, resulting in a lack of student activeness during the learning process. This study aims to determine whether there is an effect of the MURDER learning model on students' understanding of mathematical concepts. This type of research is quantitative. The research method used is an experimental research method with a Posttest Only Group Design. The research population is grade X Phase E students at SMA N 1 Lembah Melintang. Sampling was carried out using a simple random sampling technique. The sample in this study was students from class XE2 as the experimental class, totaling 33 people, and class XE4 as the control class, totaling 33 people. The research instrument used was a test of students' mathematical concept understanding abilities. The data analysis technique using the t-test obtained t_hitung=5,08 and t_tabel=1,67. While using Minitab Software obtained P_Value=0,000. Because t_hitung>t_tabel and P_Value<α with a significance level of α=0,05, H_0 is rejected. The results of the study are "There is an influence of the MURDER learning model on students' understanding of mathematical concepts."