Chemical element "Sb" (stibium) for antimony. Chemical symbols are understood internationally when element names might require translation. There have sometimes been differences in the past. For example, Germans in the past have used "J" (for the alternate name Jod) for iodine, but now use "I" and "Iod". The first letter of a chemical symbol is always capitalized, as in the preceding examples, and the subsequent letters, if any, are always lower case (small letters). Thus, the symbols for californium and einsteinium are Cf and Es. There are also symbols in chemical equations for groups of chemical elements, for example in comparative formulas.
Hilbert symbol reciprocity law follows from the Artin reciprocity law and the definition of the Hilbert symbol in terms of the Artin symbol. If "K" is a number field containing the "n"th roots of unity, "p" is a prime ideal not dividing "n", π is a prime element of the local field of "p", and "a" is coprime to "p", then the power residue symbol () is related to the Hilbert symbol by The power residue symbol is extended to fractional ideals by multiplicativity, and defined for elements of the number field by putting ()=() where ("b") is the principal ideal generated