Math 361, Spring 2015, Assignment 1

Carefully define the following terms, then give one example and one non-example of each:

1. The ring $R[x]$ (where $R$ is a commutative ring).
2. Degree of a polynomial (including the degree of the zero polynomial).
3. The field $D(x)$ (where $D$ is an integral domain).

Carefully state the following theorems (you do not need to prove them):

1. Theorem on the degree of the product of two polynomials.
2. Universal mapping property of the polynomial ring $R[x]$.

Solve the following problems:

1. Section 22, problems 7, 9, and 11.

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Questions:

Is there an equivalent theorem in the book to the Universal Mapping Property in the Theorems section?