1.

is a subring of a ring (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 is a ring homomorphism. Suppose

(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.