Exploring the Field of Non-commutative Rings

Abstract

Non-commutative rings are a type of algebraic structure that generalizes the concept of a ring, where multiplication is not necessarily commutative (i.e., the order in which you multiply elements can affect the result). This paper will delve into the world of non-commutative rings, exploring their properties, classifications, and applications in various areas of mathematics, such as abstract algebra and differential geometry.