Shreyas’ Notes

Abstract Algebra 1

MATH 356

fall, junior year

Def: bab \mid a ("bb divides aa") if a÷bZa \div b \in \mathbb{Z}

Division algorithm: a,bZa, b \in \mathbb{Z}, b>0b > 0. Then, there exist q,rZq, r \in \mathbb{Z} where 0r<b0 \leq r < b such that a=qb+ra = qb + r. Additionally, q,rq, r are unique.