  We generalize an algorithm by Goward for principalization of monomial ideals
in nonsingular varieties to work on any scheme of finite type over a field. The
normal crossings condition considered by Goward is weakened to the condition
that components of the generating divisors meet as complete intersections. This
leads to a substantial generalization of the notion of monomial scheme; we call
the resulting schemes `c.i. monomial'. We prove that c.i. monomial schemes in
arbitrarily singular varieties can be principalized by a sequence of blow-ups
at codimension 2 c.i. monomial centers.

Algebraic Geometry