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All Journal Pythagoras: Jurnal Matematika dan Pendidikan Matematika Statistika Journal of the Indonesian Mathematical Society Media Penelitian Pendidikan : Jurnal Penelitian dalam Bidang Pendidikan dan Pengajaran Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Khurul Wardati
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Industrial & Manufacturing Engineering Mathematics

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ON FREE IDEALS IN FREE ALGEBRAS OVER A COMMUTATIVE RING Wardati, Khurul; Wijayanti, Indah Emilia; Wahyuni, Sri
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.21.1.170.59-69

Abstract

Let A be a free R-algebra where R is a unital commutative ring. An ideal I in A is called a free ideal if it is a free R-submodule with the basis contained in the basis of A. The denition of free ideal and basic ideal in the free R-algebra are equivalent. The free ideal notion plays an important role in the proof of some special properties of a basic ideal that can characterize the free R-algebra. For example, a free R-algebra A is basically semisimple if and only if it is a direct sum of minimal basic ideals in A: In this work, we study the properties of basically semisimple free R-algebras.DOI : http://dx.doi.org/10.22342/jims.21.1.170.59-69
KETEGARAN REGRESI-M Khurul Wardati
STATISTIKA: Forum Teori dan Aplikasi Statistika Vol 3, No 1 (2003)
Publisher : Program Studi Statistika Unisba

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29313/jstat.v3i1.535

Abstract

Dalam model regresi linear yang umum Y = Xβ + ε, Y dan ε berdimensi n, X sebuah matriks nxp dengan xit adalahbaris-barisnya dan β berdimensi p. Permasalahan dalam analisis bregresi linear adalah bagaimana mengestimasi vektor parameterβ berdasarkan data terobservasi.Metode kuadrat terkecil dan metode maksimum likehood merupakan bentuk khusus dari estimasi M. Kedua metode tersebutmenghasilkan estimator yang sama untuk β yaitu YtXtXtX-= ( )~b . Estimator tersebut meskipun mempunyai sifat “baik”akan tetapi tidak tegar terhadap pengaruh pencilan dan asumsi distribusi.Refresi-M untuk β adalah~b yang memenuhi persamaan 0 = å=-nitxi Yi xi1y( b). Ketegaran regresi-M sangat tergantungpemilihan fungsi ψ = ρ’ dengan ρ adalah fungsi jarak. Jika diambil ρ adalah fungsi Huber misalnya. Maka akan diperolehestimator yang tegar terhadap asumsi distribusi dan pengaruh pengamatan besar.
Aljabar Semiprima Mendasar dan Aplikasinya pada Protokol Autentikasi Wardati, Khurul; Riyanto, Muhammad Zaki
PYTHAGORAS Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 1: June 2022
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/pythagoras.v17i1.48982

Abstract

Library research dengan pendekatan deduksi-induksi ini bertujuan untuk mengkaji kesemiprimaan mendasar aljabar tak bebas yang dibangun secara hingga atas ring komutatif unital.  Tujuan secara praktis penelitian ini adalah mengaplikasikan suatu contoh aljabar semiprima mendasar yang non-komutatif pada protokol autentikasi berdasarkan masalah dekomposisi. Di samping itu, aljabar semiprima mendasar lebih umum dari aljabar semiprima, hal ini ditunjukkan dengan suatu contoh penyangkal. Hasil utama dari penelitian ini adalah suatu aljabar yang dibangun secara hingga bersifat semiprima mendasar jika dan hanya jika ideal dasar nol merupakan irisan dari semua ideal dasar prima. Lebih lanjut ideal dasar nol merupakan satu-satunya ideal dasar nilpoten. Syarat perlu dan cukup ini serupa dengan sifat aljabar semiprima, dan pembuktian sifat-sifat ini pada keduanya memerlukan konsep annihilator.  The basically semiprime algebra and its application on authentication protocolAbstractThis library research is conducted with a deductive-inductive approach. The aim of this study is to explore the basically semiprimeness of the finitely generated non-free algebra over a commutative unital ring. The basically semiprime algebra is more general than a semiprime algebra, which is proven by a counterexample.  In theory, Theorem 12 is the main result of the study. The finitely generated algebra over a commutative unital ring is basically semiprime, if and only if, the zero basic ideal is the intersection of all prime basic ideals, if and only if, the zero basic ideal is the only nilpotent basic ideal. These necessary and sufficient conditions are analogous to the properties of a semiprime algebra, and proving these properties in both requires a concept of annihilator. The practical aim of this research is to apply an example of non-commutative basically semiprime algebra in an authentication protocol based on the decomposition problem.
Supporting Akreditasi LAM Teknik: Evaluasi Implementasi MBKM di Fakultas Saintek UIN Sunan Kalijaga Yogyakarta Awaliyah, Dien Fitri; Wardati, Khurul; Fatimah, Siti; Futhona, Aulia Khifah; Chasanah, Sri Istiyarti Uswatun
Media Penelitian Pendidikan : Jurnal Penelitian dalam Bidang Pendidikan dan Pengajaran Vol 17, No 1 (2023)
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/mpp.v17i1.14311

Abstract

The fulfillment of the students’ rights to study for three semesters outside study programs is one program of Merdeka Belajar-Kampus Merdeka (MBKM) or Freedom to Learn-Independent Campus policy. The MBKM program has begun to be implemented at the Faculty of Science and Technology (Saintek) UIN Sunan Kalijaga Yogyakarta for almost 4 semesters. An evaluation has been conducted using the CIPP (Context, Input, Process and Product) evaluation model to assess its effectiveness. The results of the evaluation indicate that the program has had a positive impact on student achievement, although it has not yet met the standard for LAM Engineering accreditation that is having a certain number of outbound participants with a minimum of 20 credits. However, the program is trending in a positive direction, and it is hoped that it will continue to improve and provide benefits for all stakeholders particularly in support of LAM Engineering accreditation assessments.
GRAF PRIMA KOPRIMA ATAS GRUP DIHEDRAL Shofiyulloh, M.; Munandar, Arif; Wardati, Khurul
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 16 No 2 (2024): 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.2024.16.2.13868

Abstract

A coprime prime graph over a finite group is a representation of a finite group on a graph by viewing group members as vertices of the graph and two distinct vertices and are adjacent if and only if order and order are prime or mutually prime. This research examines how to characterize the coprime prime graph over the dihedral group. Through analysis of the patterns that appear in the graphs formed, properties of coprime prime graphs over dihedral groups can be found, especially those related to the characterization of complete graphs and Hamiltonian graphs. This research also discusses the vertex connectivity of the coprime prime graph over the dihedral group.
On Basic Ideal Generated by Vertices in Cycles without Exits in Leavitt Path Algebras Wardati, Khurul; Futhona, Aulia Khifah
Journal of the Indonesian Mathematical Society Vol. 31 No. 3 (2025): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i3.1757

Abstract

Vertices located on cycles without exits have a role in constructing ideals in the Leavitt path algebras over a commutative unital ring. One key reason is that the set of such vertices is hereditary. In addition, an ideal of the commutative unital ring can be combined with these vertices to form an ideal in the Leavitt path algebra. This article focuses on creating a (basic) ideal in the Leavitt path algebras, which is generated by vertices on cycles without exits.
Co-Authors Arif Munandar Aulia Khifah Futhona Awaliyah, Dien Fitri Chasanah, Sri Istiyarti Uswatun Indah Emilia Wijayanti Riyanto, Muhammad Zaki Shofiyulloh, M. Siti Fatimah Sri Wahyuni