Prove directly that a maximal ideal is irreducible.
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- 21. Prove that if a ring has a finite number of elements, then the characteristic of is a positive integer.17. Suppose is a ring with positive characteristic. Prove that if is any ideal of then is a multiple of the characteristic of.Label each of the following statements as either true or false. The only ideals of the set of real numbers are the ideals of {0} and .