Abstract. Let M be an (R, S)-module. In this paper a generalization of the msystem set of modules to (R, S)-modules is given. Then for an (R, S)-submodule N of M , we define (R,S) √ N as the set of a ∈ M such that every m-system containing a meets N . It is shown that Kata kunci: (R, S)-modul, (R, S)-submodul prima gabungan, sistem-m, radikal prima.

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The type of this research is Research and Development. The research purpose was to develop and determine the feasibility of e-LKPD mathematics based on Problem Solving number pattern material for class VIII Junior High School. The development model used in this research is ADDIE. The subject in this research is all student of class VIII B and VIII C SMP Muhammadiyah Piyungan. The data obtained were analyzed using descriptive qualitative analysis and descriptive quantitative analysis. The results showed that e-LKPD mathematics based on Problem Solving number pattern material was feasible to use after the validation test was carried out with the material expert giving a score of 115.5 and material expert giving a score of 85.5 in the very good category. In addition, the trial of product obtained a score of 82.15 with a good category. This shows that e-LKPD mathematics based on Problem Solving number pattern material is fesiable to use in the learning.

atau m + m ∈ P . Jika M memiliki (R, S)-submodul prima-α gabungan maka radikal prima-α gabungan dari M adalah M atau merupakan irisan dari semua (R, S)-submodul prima-α gabungan di M . Pada artikel ini disajikan beberapa sifat dari radikal prima-α gabungan suatu (R, S)-modul. Lebih lanjut, pada akhir artikel ini disajikan sifat radikal prima-α gabungan pada suatu (R, S)-modul perkalian kiri.