Her contributions are core foundations of a theory of commutative rings -- one of the most important properties we usually want from a ring we study is for it t

Her contributions are core foundations of a theory of commutative rings -- one of the most important properties we usually want from a ring we study is for it to be Noetherian, which means that it satisfies certain finiteness condition, which lets one apply finite and computational methods to study it. Many important theorems in abstract algebra state properties of Noetherian rings, for instance famous Hilbert' basis theorem states that the ring of polynomials over Noetherian rings is Noetherian itself. Other important theorem, Hilbert's Nullstellensatz is frequently proved using a tool called Noether normalisation lemma. Because of that, Noetherian rings, algebras and modules are crucial to many subfields of algebra and algebraic geometry. One of her other insights, which is especially important in the field I'm interested in, was to notice that homology forms a group -- this led to explosion of new results and marked the beginning of one of the most important and influential field in XX century math, algebraic topology, as we see it today.