  We present an algebraic framework to represent indefinite nested sums over
hypergeometric expressions in difference rings. In order to accomplish this
task, parts of Karr's difference field theory have been extended to a ring
theory in which also the alternating sign can be expressed. The underlying
machinery relies on algorithms that compute all solutions of a given
parameterized telescoping equation. As a consequence, we can solve the
telescoping and creative telescoping problem in such difference rings.
