Chemical element of metals. Cu comes from Cuprum, Fe comes from Ferrum, Ag from Argentum. The symbols were not followed by a period (full stop) as with abbreviations. Later chemical elements were also assigned unique chemical symbols, based on the name of the element, but not necessarily in English. For example, sodium has the chemical symbol 'Na' after the Latin "natrium". The same applies to "W" (wolfram) for tungsten, "Fe" (ferrum) for iron, "Hg" (hydrargyrum) for mercury, "Sn" (stannum) for tin, "K" (kalium) for potassium, "Au" (aurum) for gold, "Ag" (argentum) for silver, "Pb" (plumbum) for lead, "Cu" (cuprum) for copper, and
Atomic domain ring can be "decomposed" without requiring uniqueness. The concept of an atomic domain addresses this. Let "R" be an integral domain. If every non-zero non-unit "x" of "R" can be written as a product of irreducible elements, "R" is referred to as an atomic domain. (The product is necessarily finite, since infinite products are not defined in ring theory. Such a product is allowed to involve the same irreducible element more than once as a factor.) Any such expression is called a factorization of "x". In an atomic domain, it is possible that different factorizations of the same element "x"