Some applications of the power series ring

Representation of functions as power series is a common operation in mathematical modeling. Often finding the inverse (in terms of its power series expansion) of a given function is also required. These operations are considered here in an abstract topological space- the power series ring. Some basic concepts of the commutative ring theory are discussed and the application of the abstract mathematical objects is illustrated through operation on a function expanded in power series. The case study involving the above-defined operation is the power series expansion of the scale factor that determines the dynamics of spacetime by modifying the space part of the line element.