 Even for basic rings, such as illustrated for "R" = Z at the right, the Zariski topology is quite different from the one on the set of real numbers.The spectrum contains the set of maximal ideals, which is occasionally denoted mSpec ("R").For an algebraically closed field "k", mSpec (k["T"1, ..., "T""n"] / ("f"1, ..., "f""m")) is in bijection with the set
Thus, maximal ideals reflect the geometric properties of solution sets of polynomials, which is an initial motivation for the study of commutative rings.