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## Homework Statement

Let J be the set of all polynomials with zero constant term in Z[x]. (Z=integers)

a.) Show that J is the principal ideal (x) in Z[x].

b.) Show that Z[x]/J consists of an infinite number of distinct cosets, one for each n[tex]\in[/tex]Z.

## Homework Equations

## The Attempt at a Solution

I have trouble understanding what a principal ideal is. Any help on how I should start would be great. Thanks!