ABSTRACT
In this chapter, the authors consider other algebras in which a suitable ideal can be found and look at a development where they have only a ring rather than an algebra. They also consider studies by B. Gramsch and L. A. Coburn and A. Lebow on Fredholm theory of a very general kind, the ideal being chosen arbitrarily. The authors provide an exposition of work of D. G. Schaeffer concerning the application of Breuer's theory to finite difference equations. They discuss some elementary ideas from ring theory. The authors describe the concept of order for an ideal, a notion which plays the role of dimension in ring theory. They explore some definitions and properties of C algebras of operators on a Hilbert space H.
