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    The characteristic of an integral domain help?

    Prove that the characteristic of an integral domain is either zero or prime. (using contradiction) I know I need to assume that the characteristic is not prime, but not sure how to go about that. Any help appreciated, Thanks! Also, Prove that a finite ring R cannot have characteristic zero...
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    Prove that for all n (elements of N) and a (elements of Z), the following

    statements are equivalent? Note: N = Natural Numbers, Z = Integers, Zn = Integers Modulo n (i) gcd(a,n) = 1. (ii) [a] has a multiplicative inverse in Zn. (iii) The function g: Zn --> Zn defined by g([x]) = [ax] is injective. Any help appreciated, Thanks!
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    Boolean Ring Proof Help?

    A Boolean ring R is one in which x^2 = x for all x (elements in R). (a) Prove that in a Boolean ring, every element is its own additive inverse. (Hint: Square a convenient element of R.) (b) Prove that every Boolean ring is commutative. (Hint: Square another convenient element of R. You may...
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