Valuations on a commutative ring
Valuations on a commutative ring
By a valuation on a R, we mean a pair (v, I), where r is an ordered (mult) group with a zero adjoined and v is a map of R r satisfying (1) v(xy) =v(x)v(y) for all x, yER, (2) v(x+y)?<nax{v(x),v(y)} forallx,yER. The pair will usually be denoted simply by …