Transcendental extension

In algebra, a **transcendental extension** refers to a type of field extension that contains elements that are not algebraic over the base field. More formally, if \( K \) is a field, a field extension \( L \) of \( K \) is called a transcendental extension if there exists at least one element \( \alpha \in L \) such that \( \alpha \) is not the root of any non-zero polynomial with coefficients in \( K \).