On studying bi-\(\Gamma\)-algebra and some related concepts

Abbood, Mohaimen M.; Ali Al-Fayadh, Ali Al-Fayadh; Ebrahim, Hassan H.

doi:10.22075/ijnaa.2022.5772

On studying bi-\(\Gamma\)-algebra and some related concepts

Document Type : Research Paper

Authors

Mohaimen M. Abbood ¹

Ali Al-Fayadh Ali Al-Fayadh ²

Hassan H. Ebrahim ³

¹ Ministry of Education, General Directorate of Education in Diyala, Iraq

² Department of Mathematics and Computer Applications, College of Science, Al-Nahraini University, Baghdad, Iraq

³ Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Salahaddin, Iraq

10.22075/ijnaa.2022.5772

Abstract

The aim of this research paper is to introduce the concept of bi-\(\Gamma\)-algebra space (bi-gamma algebra space). The concept of bi-\(\mu\)-measurable set in a bi-\(\Gamma\)-algebra space is defined. With this concept, some properties of bi-\(\Gamma\)-algebra space are proved. We then define various separation axioms for bi-\(\Gamma\)-algebra space such as \(M_{0},M_{1},\ M_{2},\ M_{3},\) and \(M_{4}\); then the relationships between them are studied. In addition, the concept of measurable function between two bi-measurable spaces is introduced and some results are discussed.

Keywords

algebra

( \sigma)-field

(\sigma)-algebra

(\Gamma)-algebra

measurable function

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