Prove that there is no ordering of Z/5 which makes it into an ordered ring.
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- 15. Prove that if is an ideal in a commutative ring with unity, then is an ideal in .[Type here] 23. Let be a Boolean ring with unity. Prove that every element ofexceptandis a zero divisor. [Type here]Let I be the set of all elements of a ring R that have finite additive order. Prove that I is an ideal of R.
- [Type here] 15. Give an example of an infinite commutative ring with no zero divisors that is not an integral domain. [Type here]37. Let and be elements in a ring. If is a zero divisor, prove that either or is a zero divisor.7. Prove that on a given set of rings, the relation of being isomorphic has the reflexive, symmetric, and transitive properties.