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{"ops":[{"insert":"Which of the following statements are true? Justify your answers. (This means that if you\nthink a statement is false, give a short proof or an example that shows it is false. If it is\ntrue, give a short proof for saying so.)\n(i)There is a 1 \u2013 1 correspondence between the odd permutations of S"},{"attributes":{"script":"sub"},"insert":"35"},{"insert":" the even\npermutations of S"},{"attributes":{"script":"sub"},"insert":"35."},{"insert":"\n(ii)If R is a ring such that a=\u2212a\u2200a \u2208R, then R is Boolean.\n(iii)Given any ring R, there is an ideal I of R such that "},{"attributes":{"bold":true},"insert":"R\/I"},{"insert":" is commutative.\n(iv)If S is an ideal of a ring R and f a ring homomorphism from R to a ring R', then f"},{"attributes":{"script":"super"},"insert":"-1"},{"insert":"(f(S))=S.\n(v)\u2018ring\u2019, as we now define it, was first presented to us by Dedekind.\n"}]}
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