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SUMMARY
In the course of this study we have been able to know how to add and multiply polynomials over arbitrary fields, and be able to use this to define polynomial rings, use the axioms that define a ring, and know the basic properties of rings arising from these axioms, we’ve also being able to define the Euclidian ring and we already know that a Euclidean ring is a principal ideal ring and that there are principal ideal rings which are not Euclidean rings. We’ve also being able to look at polynomial ring in one variable, add and multiply two or more polynomial rings, we also looked at some properties, direct products and the divisibility of polynomial ring, we also looked at the ideals of polynomial ring and looked at two economic application of polynomial rings namely; cyclic codes and shift register.
