Integral Domain

An integral domain is a type of mathematical structure called a ring, where you can add, subtract, and multiply elements. It has a key property: if the product of two elements is zero, then at least one of those elements must be zero. This means it has no "zero divisor" elements that multiply to zero without either being zero themselves. Integral domains are important because they resemble familiar number systems like integers, allowing for consistent algebraic manipulations without confusing factors that cancel out unexpectedly.