Marie Curie was present in such minute quantities that they would eventually have to process tons of the ore. In July 1898, Curie and her husband published a joint paper announcing the existence of an element which they named "polonium", in honour of her native Poland, which would for another twenty years remain partitioned among three empires (Russian, Austrian, and Prussian). On 26 December 1898, the Curies announced the existence of a second element, which they named "radium", from the Latin word for "ray". In the course of their research, they also coined the word "radioactivity". To prove their discoveries beyond any
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