Write A if it is always TRUE, S if it is SOMETIMES TRUE or F if it is FALSE. Please answer 1,2,3,4 and 5. 1. If R and S are isomorphic as rings, then there is a mapping from R to S whose kernel contains only the zero element in R. 2. If F is a field and u,v are algebraic over F, then v is algebraic over F(u). 3. If F is a field and f∈F[x] with degree at least 1, then there is a field K for which F≤K and f has a root in K.

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Q: (a) Let R be a ring, a € R and define AR = {r € R | ar = OR} where OR ER is the zero element of R.…

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