Skew Field

A skew field, also called a division ring, is a mathematical structure similar to a field but where multiplication may not be commutative—that is, the order of multiplication matters. In a skew field, you can add, subtract, multiply, and divide (except by zero), and all these operations follow certain rules. Unlike regular fields (like rational or real numbers), in a skew field, multiplying two elements might give different results depending on which order they are multiplied. Skew fields are important in advanced algebra and have applications in areas like number theory and geometry.