1. $\displaystyle R = \{ a +bi : a,b \in Z \}$

is a subring of a ring $\displaystyle C$ (complex)

Find an element of R different from the identity element which has a multiplicative inverse in R.

2. Let R,S be rings and suppose $\displaystyle f:R \rightarrow S$ is a ring homomorphism. Suppose $\displaystyle im(f) = S $

(a) Show that if R has an identity element then S has an identity element.

(b) Show that if R is commutative then S is commutative

(C) Is it true that if R is an integral domain then S is an integral domain? Justify your assertion.

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I'm not 100% sure on some of this.