Abstract Algebra/Polynomial Rings

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Although there is a theory of non-commutative polynomial rings, it presents some difficulties and will not be treated on this page. Thus, we will work only with commutative rings for their polynomial rings.

The degree of a polynomial is defined to be . If is a field, and and are polynomials of , then we can divide by to get . However, we can also do this for any arbitrary ring if the leading coefficient of is 1.