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- 15. Prove that if is an ideal in a commutative ring with unity, then is an ideal in .Let I be an ideal in a ring R with unity. Prove that if I contains an element a that has a multiplicative inverse, then I=R.Label each of the following statements as either true or false. The only ideal of a ring R that property contains a maximal ideal is the ideal R.
- a. If R is a commutative ring with unity, show that the characteristic of R[ x ] is the same as the characteristic of R. b. State the characteristic of Zn[ x ]. c. State the characteristic of Z[ x ].True or False Label each of the following statements as either true or false. Every ideal of a ring is a subring of.True or false Label each of the following statements as either true or false. 3. The only ideal of a ring that contains the unity is the ring itself.