True or False without explanation If R and S are integral do

True or False (without explanation): If R and S are integral domains then R times S is also an integral domain. Z_4 times Z_6 is isomorphic to Z_24. If R is a subfield of a field S then I_R = l_s. If f: R rightarrow S and g: S rightarrow T are homomorphisms then the composition g o f: R rightarrow T is also a homomorphism of rings. (Recall that (g o f) (r) = g(f(r)) for all r elementof R.) If R and S are commutative rings with identity then all units of R times S are of the form (u, v) with u a unit in R and v a unit in S. Z_5 times Z_7 is isomorphic to Z_35. Let F be a field. If f(x) and g(x) in F[x] have the same roots in F, then f(x) and g(x) are associates in F[x]. If R is a commutative ring and a_0 + a_1 x + ... a_n x^n a zero-divisor in R[x] with a_n notequalto 0_R, then a_n is a zero-divisor in R.

Solution

Answer for each point without explanations

Explatio

a)Yes

b)Yes

c)No

d)Yes

e)Yes

f)Yes

g)Yes