- #1

Oxymoron

- 870

- 0

**Questions**

**1) Let [itex]x^2-x+1[/itex] be the ideal for [itex]\mathbb{R}[x][/itex] generated by the polynomial [itex]x^2-x+1[/itex]. Show that the quotient ring [itex]\mathbb{R}[x]/(x^2-x+1)[/itex] is isomorphic to the field [itex]\mathbb{C}[/itex] of complex numbers.**

**2) Show that the polynomial [itex]x^2+x+1[/itex] is irreducible over [itex]\mathbb{Z}_2[/itex].**