An algebraic integer of the form a + b sqrt(D) where D is squarefree forms a quadratic field and is denoted Q(sqrt(D)). If D>0, the field is called a real quadratic field, and if D<0, it is called an imaginary quadratic field. The integers in Q(sqrt(1)) are simply called "the" integers. The integers in Q(sqrt(-1)) are called Gaussian integers, and the integers in Q(sqrt(-3)) are called Eisenstein integers. The algebraic integers in an arbitrary quadratic field do not necessarily have unique factorizations. For example, the fields Q(sqrt(-5)) and Q(sqrt(-6)) are not uniquely factorable, since

algebraic integer | Eisenstein integer | Gaussian integer | imaginary quadratic field | integer | number field | quadratic | real quadratic field