Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In abstract algebra, a field extension L/K is called algebraic if every element of L is algebraic over K, i.e. if every element of L is a root of some non-zero polynomial with coefficients in K. Field extensions which are not algebraic, i.e. which contain transcendental elements, are called transcendental. For example, the field extension R/Q, that is the field of real numbers as an extension of the field of rational numbers, is transcendental, while the field extensions C/R and Q(âˆš2)/Q are algebraic, where C is the field of complex numbers. All transcendental extensions are of infinite degree.