ABSTRACT
A field is a commutative ring with identity, in which every non-zero element is invertible. More informally, a field F is a set with two commutative operations (addition and multiplication), in which one can add, subtract, and multiply any two elements, divide any element by any non-zero element, and the multiplication operation distributes over addition. It is a convention to disregard the zero ring (the ring with 0 = 1) as a field.
