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All Journal FIBONACCI: Jurnal Pendidikan Matematika dan Matematika Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Muhammad Ali Rizqan
Universitas Lambung Mangkurat, Indonesia
Education Mathematics

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Modul Tergeneralisasi penuh Muhammad Ali Rizqan
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 18 No 1 (2026): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2026.18.1.19604

Abstract

This paper introduces the concept of fully generalized modules as an extension of classical module theory over generalized algebraic structures. We prove that every fully generalized module forms a normal generalized group and contains abelian subsets. We further establish the existence of a trivial fully generalized submodule and show that the family of fully generalized submodules is closed under sums and intersections. In addition, we prove the existence of fully generalized module homomorphisms and derive their elementary properties. These results extend existing work on generalized modules and provide a broader theoretical framework for studying module-like structures in generalized algebra. Potential directions for future research include the study of direct sums, fully generalized torsion modules, and fully generalized vector spaces. Keywords: Generalized group, generalized ring, fully generalized module, submodule, homomorphism..
PCA-Based Dimensionality Reduction and Logistic Regression Modeling of Students’ GPA Na’imah Hijriati; Rikha Syahda; Aprida Siska Lestia; Mochammad Idris; Muhammad Ali Rizqan; Abdul Rasyid Nasyar
FIBONACCI: Jurnal Pendidikan Matematika dan Matematika Vol. 12 No. 1 (2026): FIBONACCI: Jurnal Pendidikan Matematika dan Matematika
Publisher : Fakultas Ilmu Pendidikan Universitas Muhammadiyah Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24853/fbc.12.1.99-112

Abstract

This study investigated the effects of socioeconomic, motivational, and psychological factors on students’ academic performance using dimensionality reduction and predictive modeling. Principal Component Analysis was applied to reduce 29 observed variables into latent components based on eigenvalues and explained variance criteria. Logistic regression was then used to model the probability of achieving a high Grade Point Average (GPA). The results showed that psychological components were the most significant predictors, with four out of five psychological components being statistically significant, while only one socioeconomic component was significant. The model demonstrated good fit with a Nagelkerke  of  and classification accuracy of . These findings indicated that psychological support played a dominant role in predicting academic performance, suggesting that interventions focusing on mental and emotional factors could improve students’ academic outcomes.
Co-Authors Abdul Rasyid Nasyar Aprida Siska Lestia Mochammad Idris Na’imah Hijriati Rikha Syahda