This is the first out of two papers on independent resolutions for totally
disconnected dynamical systems. In the present paper, we discuss independent
resolutions from an algebraic point of view. We also present applications to
group homology and cohomology. This first paper sets the stage for our second
paper, where we explain how to use independent resolutions in K-theory
computations for crossed products attached to totally disconnected dynamical
systems.Comment: 26 pages; minor changes improving the expositio
