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ON JOINTLY PRIME RADICALS OF (R,S)-MODULES Yuwaningsih, Dian Ariesta; Wijayanti, Indah Emilia
Journal of the Indonesian Mathematical Society Volume 21 Number 1 (April 2015)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.21.1.199.25-34

Let $M$ be an $(R,S)$-module. In this paper a generalization of the m-system set of modules to $(R,S)$-modules is given. Then for an $(R,S)$-submodule $N$ of $M$, we define $\sqrt[(R,S)]{N}$ as the set of $a\in M$ such that every m-system containing $a$ meets $N$. It is shown that $\sqrt[(R,S)]{N}$ is the intersection of all jointly prime $(R,S)$-submodules of $M$ containing $N$. We define jointly prime radicals of an $(R,S)$-module $M$ as $rad_{(R,S)}(M)=\sqrt[(R,S)]{0}$. Then we present some properties of jointly prime radicals of an $(R,S)$-module.DOI :Â http://dx.doi.org/10.22342/jims.21.1.199.25-34

On Fully Prime Radicals Wijayanti, Indah Emilia; Yuwaningsih, Dian Ariesta
Journal of the Indonesian Mathematical Society Volume 23 Number 2 (October 2017)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.23.2.302.33-45

In this paper we give a further study on fully prime submodules. For any fully prime submodules we define a product called $\am$-product. The further investigation of fully prime submodules in this work, i.e. the fully m-system and fully prime radicals, is related to this product. We show that the fully prime radical of any submodules can be characterize by the fully m-system. As a special case, the fully prime radical of a module $M$ is the intersection of all minimal fully prime submodules of $M$.

Some Properties of Left Weakly Jointly Prime (R,S)-Submodules Yuwaningsih, Dian Ariesta
Journal of the Indonesian Mathematical Society Volume 26 Number 2 (July 2020)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.26.2.832.234-241

Let R and S be commutative rings with identity. A proper (R,S)submodule P of M is called a left weakly jointly prime if for each element a and b in R and (R,S)-submodule K of M with abKS âŠ† P implies either aKS âŠ† P or bKS âŠ† P. In this paper, we present some properties of left weakly jointly prime (R,S)-submodule. We show some necessary and sufficient condition of left weakly jointly prime (R,S)-submodule. Moreover, we present that every left weakly jointly prime (R,S)-submodule contains a minimal left weakly jointly prime (R,S)submodule. At the end of this paper, we also show that in left multiplication (R,S)-module, every left weakly jointly prime (R,S)-submodule is equal to jointly prime (R,S)-submodules.

PENGEMBANGAN E-LKPD MATEMATIKA BERBASIS PROBLEM SOLVING POKOK BAHASAN POLA BILANGAN Muhammad Alfian Darmawan; Dian Ariesta Yuwaningsih
JURNAL PENDIDIKAN MATEMATIKA UNIVERSITAS LAMPUNG Vol 9, No 4 (2021): DESEMBER 2021
Publisher : Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar

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. Keywords: ADDIE; e-LKPD Mathematics; problem solving DOI: http://dx.doi.org/10.23960/mtk/v9i4.pp343-359

Algebraic Structure of Supernilpotent Radical Class Constructed from a Topology Thychonoff Space Puguh Wahyu Prasetyo; Dian Ariesta Yuwaningsih; Burhanudin Arif Nurnugroho
Al-Jabar: Jurnal Pendidikan Matematika Vol 11, No 2 (2020): Al-Jabar: Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

A radical class of rings is called a supernilpotent radicals if it is hereditary and it contains the class for some positive integer In this paper, we start by exploring the concept of Tychonoff space to build a supernilpotent radical. Let be a Tychonoff space that does not contain any isolated point. The set of all continuous real-valued functions defined on is a prime essential ring. Finally, we can show that the class of rings is a supernilpotent radical class containing the matrix ring .

ON JOINTLY PRIME RADICALS OF (R,S)-MODULES Dian Ariesta Yuwaningsih; Indah Emilia Wijayanti
Journal of the Indonesian Mathematical Society Volume 21 Number 1 (April 2015)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.21.1.199.25-34

Let $M$ be an $(R,S)$-module. In this paper a generalization of the m-system set of modules to $(R,S)$-modules is given. Then for an $(R,S)$-submodule $N$ of $M$, we define $\sqrt[(R,S)]{N}$ as the set of $a\in M$ such that every m-system containing $a$ meets $N$. It is shown that $\sqrt[(R,S)]{N}$ is the intersection of all jointly prime $(R,S)$-submodules of $M$ containing $N$. We define jointly prime radicals of an $(R,S)$-module $M$ as $rad_{(R,S)}(M)=\sqrt[(R,S)]{0}$. Then we present some properties of jointly prime radicals of an $(R,S)$-module.DOI : http://dx.doi.org/10.22342/jims.21.1.199.25-34

On Fully Prime Radicals Indah Emilia Wijayanti; Dian Ariesta Yuwaningsih
Journal of the Indonesian Mathematical Society Volume 23 Number 2 (October 2017)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.23.2.302.33-45

In this paper we give a further study on fully prime submodules. For any fully prime submodules we define a product called $\am$-product. The further investigation of fully prime submodules in this work, i.e. the fully m-system and fully prime radicals, is related to this product. We show that the fully prime radical of any submodules can be characterize by the fully m-system. As a special case, the fully prime radical of a module $M$ is the intersection of all minimal fully prime submodules of $M$.

Some Properties of Left Weakly Jointly Prime (R,S)-Submodules Dian Ariesta Yuwaningsih
Journal of the Indonesian Mathematical Society Volume 26 Number 2 (July 2020)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.26.2.832.234-241

Let R and S be commutative rings with identity. A proper (R,S)submodule P of M is called a left weakly jointly prime if for each element a and b in R and (R,S)-submodule K of M with abKS ⊆ P implies either aKS ⊆ P or bKS ⊆ P. In this paper, we present some properties of left weakly jointly prime (R,S)-submodule. We show some necessary and sufficient condition of left weakly jointly prime (R,S)-submodule. Moreover, we present that every left weakly jointly prime (R,S)-submodule contains a minimal left weakly jointly prime (R,S)submodule. At the end of this paper, we also show that in left multiplication (R,S)-module, every left weakly jointly prime (R,S)-submodule is equal to jointly prime (R,S)-submodules.

Pengembangan Modul Matematika dengan Pendekatan Saintifik Pokok Bahasan Vektor Sri Hidayati; Dian Ariesta Yuwaningsih
Buana Matematika : Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 11 No 2 (2021)
Publisher : Universitas PGRI Adi Buana Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36456/buanamatematika.v11i2.3293

Penelitian ini dilakukan dengan tujuan menghasilkan produk pengembangan bahan ajar berupa modul dengan pendekatan saintifik pokok bahasan vektor dan untuk mengetahui kelayakan modul dengan pendekatan saintifik pada pokok bahasan vektor. Peneliti merupakan penelitian pengeembangan dengan model pengembangan ADDIE. Penelitian ini dilakukan di SMA Muhammadiyah 3 Yogyakarta dengan subyek penelitian terdiri atas ahli materi, ahli media, dan peserta didik kelas XI MIPA SMA Muhammadiyah 3 Yogyakarta. Teknik pengumpulan data dilakukan dengan observasi, wawancara, dan penyebaran angket. Berdasarkan hasil analisis data, diperoleh bahwa penilaian ahli materi termasuk dalam kategori sangat baik dengan nilai rata-rata 89.5, sedangkan penilaian dari ahli media dalam kategori sangat baik dengan nilai rata-rata 84. Sedangkan, penilaian respon peserta didik mendapatkan nilai rata-rat 79,2 dalam kategori baik. Dengan demikian, modul matematika dengan pendekatan saintifik pada pokok bahsan vektor ini layak digunakan dalam proses pembelajaran.

Pelatihan Pembelajaran Daring Menggunakan Google Classroom di SMP Muhammadiyah Se-Kecamatan Pleret Dian Ariesta Yuwaningsih; Rusmining Rusmining
Surya Abdimas Vol. 5 No. 3 (2021)
Publisher : Universitas Muhammadiyah Purworejo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37729/abdimas.v5i3.1111

Pada era pandemi saat ini, pembelajaran di Indonesia dilakukan secara daring. Salah satu aplikasi pembelajaran daring yang mudah dan praktis diakses oleh berbagai kalangan adalah Google Classroom. Berdasarkan hasil wawancara terhadap beberapa pendidik matematika di SMP Muhammadiyah Pleret dan MBS Pleret diketahui bahwa para pendidik matematika di sana belum ada yang memanfaatkan pembelajaran daring seperti Google Classroom. Pendidik masih belum mengenal Google Classroom. Saat ini, para pendidik melakukan pembelajaran daring dengan menggunakan Google Form. Kegiatan Program Kemitraan Masyarajat (PKM) ini memiliki tujuan memberikan pelatihan dan pendampingan pembelajaran daring menggunakan Google Classroom bagi pendidik matematika di SMP Muhammadiyah se-kecamatan Pleret. Kegiatan PKM ini dilaksanakan secara daring melalui aplikasi Google Meet pada tanggal 14-16 Oktober 2020. Peserta kegiatan PKM ini terdiri atas semua pendidik matematika sebanyak 10 orang yang meliputi pendidik di SMP Muhammadiyah Pleret dan pendidik di MBS Pleret. Kegiatan ini menggunakan metode penyuluhan, pelatihan, dan pendampingan. Hasil dari kegiatan ini adalah sebanyak 93% pendidik matematika sangat setuju serta 7% pendidik matematika setuju dengan diadakannya kegiatan pelatihan pembelajaran daring menggunakan Google Classroom. Dengan demikian, kegiatan ini memberikan manfaat bagi para pendidik matematika di SMP Muhammadiyah se-kecamatan Pleret.

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