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- 21. Prove that if a ring has a finite number of elements, then the characteristic of is a positive integer.Prove that if a is a unit in a ring R with unity, then a is not a zero divisor.Prove that any field that contains an intergral domain D must contain a subfield isomorphic to the quotient field Q of D.
- [Type here] 15. Give an example of an infinite commutative ring with no zero divisors that is not an integral domain. [Type here]15. In a commutative ring of characteristic 2, prove that the idempotent elements form a subring of .27. If is a commutative ring with unity, prove that any maximal ideal of is also a prime ideal.