Answer to Question #203288 in Abstract Algebra for Raghav

Question

Which of the following statements are true? Justify your answers. (This means that if you

think a statement is false, give a short proof or an example that shows it is false. If it is

true, give a short proof for saying so.)

(i)There is a 1 – 1 correspondence between the odd permutations of S₃₅ the even

permutations of S_35.

(ii)If R is a ring such that a=−a∀a ∈R, then R is Boolean.

(iii)Given any ring R, there is an ideal I of R such that R/I is commutative.

(iv)If S is an ideal of a ring R and f a ring homomorphism from R to a ring R', then f^-1(f(S))=S.

(v)‘ring’, as we now define it, was first presented to us by Dedekind.

Answer 1

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