Marie Curie doubt, the Curies sought to isolate polonium and radium in pure form. Pitchblende is a complex mineral; the chemical separation of its constituents was an arduous task. The discovery of polonium had been relatively easy; chemically it resembles the element bismuth, and polonium was the only bismuth-like substance in the ore. Radium, however, was more elusive; it is closely related chemically to barium, and pitchblende contains both elements. By 1898 the Curies had obtained traces of radium, but appreciable quantities, uncontaminated with barium, were still beyond reach. The Curies undertook the arduous task of separating out radium salt by differential
Field with one element objects. While there is still no field with a single element in these theories, there is a field-like object whose characteristic is one. F cannot be a field because all fields must contain two distinct elements, the additive identity zero and the multiplicative identity one. Even if this restriction is dropped, a ring with one element must be the zero ring, which does not behave like a finite field. Instead, most proposed theories of F replace abstract algebra entirely. Mathematical objects such as vector spaces and polynomial rings can be carried over into these new theories by mimicking their abstract