Valuation domains are integral domains that are characterized by the existence of a valuation, which assigns a value to each element in a way that captures the 'size' or 'multiplicative structure' of the elements. This concept connects to discrete valuations and valuation rings as it helps in understanding the structure of these rings, allowing for a classification of their ideals and facilitating the study of local properties in algebraic number theory.
congrats on reading the definition of Valuation Domains. now let's actually learn it.