in these epochs, she was not merely applying ideas and methods of earlier mathematicians; rather, she was crafting new systems of mathematical definitions that would be used by future mathematicians. in particular, she developed a completely new theory of ideals in rings, generalizing earlier work of richard dedekind. she is also renowned for developing ascending chain conditions, a simple finiteness condition that yielded powerful results in her hands. such conditions and the theory of ideals enabled noether to generalize many older results and to treat old problems from a new perspective, such as elimination theory and the algebraic varieties that had been studied by her father.