if $r$ is a commutative ring and $i$ an ideal, the associated graded ring ${\rm gr}\, r := r/i + i/i^2 + i^2/i^3 + \ldots$ is a very useful replacement for $r$ for many algebraic and geometric purposes. frequently, though, it will have nilpotent elements even when $r$ didn't. \vskip .1in \noindent i'll discuss a replacement for it, essentially due to samuel, rees, and nagata, using the ``homogenization" of the $i$-adic filtration. this new filtration is better geometrically motivated, and its associated graded ring never has nilpotents. \vskip .1in \noindent the applications include nilpotent-free versions of intersection theory on smooth varieties, and of gr\"obner bases.