Ring of integers

The ring of integers in a number field is the set of all numbers within that field that satisfy polynomial equations with whole number coefficients, similar to how ordinary integers work within rational numbers. It generalizes the concept of integers to more complex number systems, capturing elements that behave like whole numbers but may include roots and other algebraic numbers. These integers form a structured mathematical system, called a ring, allowing mathematicians to study properties like divisibility and factors in these extended contexts, much like how integers function within the rational numbers.