n. 1. a set of entities subject to two binary operations, usually referred to as addition and multiplication, such that the set is a commutative group under the addition, the set excluding the zero element is a commutative group under the multiplication, and the multiplication distributes over the addition; thus the rationals and the reals are fields but the integers are not. See also skew field. Compare group, ring, algebraic number field. 2. the set of elements that are either arguments or values of a function, the union of its domain and range. 3. see vector field, scalar field, tensor field.