On the Non-Commutative Logical Rings As Novel Extensions of Neutrosophic Rings

Murat Ozcek

Gaziantep University, Department of Mathematics, Gaziantep, Turkey

Abstract

This paper uses some logical algebraic elements to extend any ring into a non-commutative ring containing the original ring with many generalized substructures and special elements. On the other hand, we study the substructures of non-commutative logical rings such as AH-homomorphisms and AH-ideals with many examples that explain their algebraic validity. Also, we discuss the possibility of solving a linear Diophantine equation with two variables in the non-commutative logical ring of integers, where we present an easy algorithm to solve this kind of generalized Diophantine equation.

Keywords: neutrosophic ring; non-commutative; AH-ideal; AH-homomorphism.