  In the current article we study structure of a Chevalley group $G(R)$ over a
commutative ring $R$. We generalize and improve the following results: (1)
standard, relative, and multi-relative commutator formulas; (2) nilpotent
structure of [relative] $K_1$; (3) bounded word length of commutators. To this
end we enlarge the elementary group, construct a generic element for the
extended elementary group, and use localization in the universal ring. The key
step is a construction of a generic element for a principle congruence
subgroup, corresponding to a principle ideal.
