A valued field is a field equipped with a valuation that assigns a size or 'value' to each element, which helps measure the 'distance' between elements. This concept plays an essential role in understanding algebraic structures and geometric properties, especially in relation to the tropical Nullstellensatz, where valuations provide a way to relate algebraic varieties and their solutions in a tropical context. Valued fields are foundational in translating classical algebraic geometry into the realm of tropical geometry.
congrats on reading the definition of valued field. now let's actually learn it.