Ring Theory 5: Zero Divisors and Integral Domains скачать в хорошем качестве

Ring Theory 5: Zero Divisors and Integral Domains

Intuition behind zero divisors, and rings without zero divisors. Practice problems: 1) Find all units of Z_20, and find all zero divisors of Z_20. Do you see a relationship between them? 2) Show that every nonzero element of Z_n is either a unit or a zero divisor. 3) Let d be a fixed integer. Prove that the set {a + b*sqrt(d) | a,b are integers} is an integral domain (under normal addition and multiplication). 4) Cancellation property: Let a,b,c be elements of an integral domain such that a is not zero. Prove that if ab=ac, then b=c. (Note: we didn't assume a is a unit)