Problem 1E

Verify that Examples 1 through 8 are as claimed.

Reference:

EXAMPLE 1 The ring of integers is an integral domain

EXAMPLE 2 The ring of Gaussian integers Z[i] = {a + bi | a, b ∈ Z} is an integral domain.

EXAMPLE 3 The ring Z[x] of polynomials with integer coefficients is an integral domain.

EXAMPLE 4 The ring is an integral domain.

EXAMPLE 5 The ring Zp of integers modulo a prime p is an integral domain.

EXAMPLE 6 The ring Zn of integers modulo n is not an integral domain when n is not prime.

EXAMPLE 7 The ring M2(Z) of 2 × 2 matrices over the integers is not an integral domain.

EXAMPLE 8 Z ⊕ Z is not an integral domain.

Lowery 1 Katrina Lowery EN 110382 Antoinette Hayden 6 October, 2016 “Don’t Blame the Eater”: Stating the Facts This article “Don’t Blame the Eater” by David Zinczenko starts off with saying that the topic of this article would be titled in a newspaper headline for Jay Leno’s monologue. Zinczenko’s article debates about how the fast food industry is affecting children. It discusses his experiences with fast foods during his childhood and how it is causing children to develop health problems at an early age. Since the author has had experience with this topic and had a lot of information to back him up, this article is quite effective because Zinczenko explains to the readers why fast food is unhealthy by using facts, emotional appea