A field without its elements is generally referred to as an "abstract field" or a "field structure." In mathematics, a field is a specific algebraic structure consisting of a set of elements along with two operations, addition and multiplication, which satisfy certain properties.
An abstract field or field structure focuses on the algebraic properties and axioms of a field, without explicitly specifying the elements of the field. Instead of working with specific numbers or objects, the abstract field considers the properties and rules that apply to elements within a field. This approach allows for the study of general properties applicable to various specific fields.
By defining the properties and axioms of a field, mathematicians can explore the fundamental characteristics of fields without needing to specify the actual elements involved. This abstraction provides a framework to examine the properties and relationships that hold within fields as a whole, regardless of the specific elements they may contain.