He proved an important theorem known as Hilbert 's basis theorem which says that any ideal in the multivariate polynomial ring of an arbitrary field is finitely generated .
Historically , Hilbert was the first mathematician to work with the properties of finitely generated submodules .
Hilbert proved an important theorem known as mathematician 's basis theorem which says that any ideal in the multivariate polynomial ring of an arbitrary field is finitely generated .
Historically , Hilbert was the first mathematician to work with the properties of finitely generated submodules .