Complex sentence: Two valuations are said to be equivalent if they are proportional (i.e. they differ by a fixed element in\\ mathfrak): every equivalence class of valuations on a field\\ mathbb is called a place.
Split into simpler sentences: Two valuations are said to be equivalent if they are proportional (i.e. they differ by a fixed element in\\ mathfrak). An equivalence class of valuations on a field\\ mathbb is called a place.