Semeton Mathematics Journal

Study of Primality in Modules: Prime, Weakly Prime, Almost Prime, and n-Almost Prime Submodules

Jinan Ambar, Muhammad Afdhaluzzikri — Wed, 02 Oct 2024 00:00:00 +0100

Module theory, as a branch of abstract algebra, is a field of study that extends the concept of vector spaces into a more general framework, finding broad applications across various mathematical fields. The concept of prime numbers, initially abstracted by Dedekind in the form of prime ideals, underwent further development by mathematicians. Anderson generalized it into weak prime ideals, while Sharma developed the concept of nearly prime ideals. After Noether introduced the concept of modules, Dauns brought this primality notion into module theory under the name of prime submodules. Subsequently, Khashan generalized it into weak and nearly prime submodules. The latest development came from Azizi, who introduced the concept of nearly prime submodules into n-nearly prime submodules. In this context, this article discusses several key characteristics of prime submodules and their generalizations, providing a deep understanding of their fundamental structures and properties. Through this understanding, we can explore various applications of module theory in various mathematical contexts and delve into the complexities inherent in the study of primality and submodule structures within modules. The purpose of this research is to explain some structures and properties of prime submodules. This research uses the literature review method, which is by collecting information from various reading sources related to prime submodules and their generality. The result of this research is an explanation of some structures and properties of prime submodules and their examples.

Some Characteristics of Submodules of Module

Muhammad Afdhaluzzikri, Jinan Ambar — Wed, 02 Oct 2024 00:00:00 +0100

In the context of group cohomology, free modules are used to construct projective resolutions, while torsion modules play a significant role. In the theory of invariants, free modules describe all polynomial invariants, whereas torsion modules are relevant in the study of modular invariants. In elliptic curve cryptography, torsion points ensure security, with free modules used for arithmetic operations. The article also discusses the structure and properties of submodule types such as torsion, free, indecomposable, cyclic, and pure submodules, highlighting the importance of understanding the various applications of free and torsion modules.

Solving Irreducible Polynomials over Zp and GCD, LCM of Two Polynomials over Fn Using Python

Yudha Sakti Nusantara, Wahyu Maulana — Mon, 07 Oct 2024 00:00:00 +0100

This research aims to solve the irreducible polynomial problem over finite field Zp and determine the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two polynomials over finite field Fn using Python programming language. In the digital age, programming plays an important role in various disciplines. Python, with its simple syntax and computational libraries like SymPy, has become a top choice among the various programming languages available. Polynomials appear frequently in the computer field, especially in cryptographic algorithms, data compression, and error coding. This research utilizes Euclid's Algorithm to determine the GCD and LCM of two polynomials over a finite field Fn, as well as evaluate the irreducibility of polynomials over a finite field Zp. Determining irreducibility is very important in polynomial theory and is a challenging task if done manually. With the help of Python, this research produces a script or syntax that is able to automate the process, thus saving time and reducing complexity. The final result of this research is an effective Python script or syntax to determine the GCD and LCM of two polynomials over Fn, as well as evaluate whether a polynomial is reducible or irreducible over Zp.

Modeling Maternal Mortality Rate (MMR) In Indonesia Using Mixed Geographically Weighted Regression (MGWR)

Tamsilul Lawwamah, Lisa Harsyiah, Qurratul Aini — Mon, 14 Oct 2024 00:00:00 +0100

Maternal Mortality Rate (MMR) is on of the targets for a achieving the Sustainable Development Goals (SDGs). The aim of this research is to find the right model for estimating MMR and to look at the factors that influence MMR in Indonesia. Estimation were carried out using the Mixed Geographically Weigthed Regression (MGWR) model. The MGWR model is a combination of GWR and linear regression with variables that having influence locally and some globally. The results obtained are that the MGWR model is superior the GWR model, because the smallest AIC value for MGWR is 463,0564. Factors that have significant influence using the adaptive Gaussian kernel weighting are postpartum mothers (x4) , postpartum mothers receiving vitamin A (x5), giving Fe3 tablets to pregnant women (x6) , and handling obstetric complications (x7).

Quality Control Of Packaged Drinking Water Production Using Control Chart Decision On Belief

Nur Halifatunnisa, Zulhan Widya Baskara, Lisa Harsyiah — Tue, 15 Oct 2024 00:00:00 +0100

The most popular drinking water product produced by PT.X is the 220 ml glass packaging product. This product experienced the most production defects at 0.086% of total production. Based on observations that have been made, there are several problems that cause defective products, such as damaged packaging and poor water quality. So PT.X in maintaining production quality must improve the process of maintaining quality control. The aim of this research is in line with the problems faced by PT.X, namely controlling the quality of bottled drinking water using a decision on belief control chart. Control charts are used to monitor whether product defect data is statistically controlled or not. One of the control charts used to monitor whether product defect data is statistically controlled or not is the Decision on Belief control chart, because the Decision on Belief control chart is more sensitive to data shifts so that faster in detecting data that goes outside control limits or is out of control. Based on the graph of the results of the decision on belief control chart, of the 25 data there are 24 data that are out of the upper control limit and the lower control limit, meaning that the decision on belief control chart is sensitive to data shifts in detecting out of control data. Based on the results of the average run length calculation, it is concluded that the decision on belief control chart is weak in detecting out of control data because the shift value obtained is getting bigger.

Design of Facial Expressions Recognition for Academic Presence By Using Backpropagation Artificial Neural Networks Based on Principal Components Analysis

Tue, 15 Oct 2024 00:00:00 +0100

There are 4,004 universities in Indonesia where each university needs data to find out student activities, one of which is through attendance. Some universities in Indonesia still use manual attendance systems and attendance systems through the website. This system has several obstacles that require solutions. Therefore, a more concise system is needed to assist students in filling in the attendance. This research aims to make a design to make academic presence for students by using neural network. There are many methods that can be used to create this system including using Principal Component Analysis (PCA) based on Backlpropagation Neural Network (BNN) because it can help the system perform faster and more accurately without losing important information. After carrying out a series of steps of algorithm designed for student attendance, we get the recognition of facial image expressions by using ANN Backpropagation and recognition of facial image expression with PCA.