generalization algebraic geometry introduced grothendieck many notions commutative algebra counterparts geometrical notions occurring algebraic geometry case krull dimension primary decomposition regular rings cohen macaulay rings gorenstein rings many notions history subject first known ideal theory began richard dedekind 's work ideals based earlier work ernst kummer leopold kronecker later david hilbert introduced term ''ring'' generalize earlier term ''number ring'' hilbert introduced abstract approach replace concrete computationally oriented methods
Formal science Mathematics Pure mathematics Algebra Commutative algebra