Testing Division Rings and Fields Using a Computer Program

Abstract algebra is a branch of mathematics which is studying algebraic structures of sets with respect to some operations on them. Each structure has its own axioms and properties. In some cases, to test what kind of structure is a given set and operations is difficult to be done manually. To help this, an application program to test algebraic structures is developed. In this article, we focus on two structures: division ring and fields, and an application program to test them is created by using Java, an open-source based programming language. This application program provides testing of various input of finite set such as integers, matrices and alphabets. By this application, testing of algebraic structures can be done faster than the manual one and its results are accurate. In this article, we focus on testing division rings and fields, together with some examples.