algebraic extension

== English == === Noun === algebraic extension (plural algebraic extensions) (algebra, field theory) A field extension L/K which is algebraic over K (i.e., is such that every element of L is a root of some (nonzero) polynomial with coefficients in K). ==== Usage notes ==== A field extension that contains elements that are not algebraic is called transcendental. ==== Hypernyms ==== associative algebra ==== Hyponyms ==== normal extension separable extension Galois extension === Further reading === Integral element on Wikipedia.Wikipedia Galois extension on Wikipedia.Wikipedia Separable extension on Wikipedia.Wikipedia Normal extension on Wikipedia.Wikipedia Field extension on Wikipedia.Wikipedia