  Discrete tomography is concerned with the reconstruction of images that are
defined on a discrete set of lattice points from their projections in several
directions. The range of values that can be assigned to each lattice point is
typically a small discrete set. In this paper we present a framework for
studying these problems from an algebraic perspective, based on Ring Theory and
Commutative Algebra. A principal advantage of this abstract setting is that a
vast body of existing theory becomes accessible for solving Discrete Tomography
problems. We provide proofs of several new results on the structure of
dependencies between projections, including a discrete analogon of the
well-known Helgason-Ludwig consistency conditions from continuous tomography.
