The algebraic structure which is a substructure of the extension structure
The algebraic structure which is an extension of the base structure
The dimension of the extension structure as a vector space over the base structure (optional for extensions of Q, R, or C)
The basis vectors of the extension structure (optional for extensions of Q, R, or C)
Whether the extension structure is finite or not (optional for extensions of Q, R, or C)
Whether the extension structure is simple or not (optional for extensions of Q, R, or C)
Whether the extension structure is algebraic or not (optional for extensions of Q, R, or C)
Defines an algebraic structure extension known as a field extension.