Consider the ideal N=<4> of the ring Z24. How many elements does the quotient ring Z24/N have?
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Consider the ideal N=<4> of the ring Z24. How many elements does the quotient ring Z24/N have?
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- 24. If is a commutative ring and is a fixed element of prove that the setis an ideal of . (The set is called the annihilator of in the ring .)18. Let be a commutative ring with unity, and let be the principal ideal in . Prove that is isomorphic to .27. If is a commutative ring with unity, prove that any maximal ideal of is also a prime ideal.
- Let R be a commutative ring that does not have a unity. For a fixed aR, prove that the set (a)={na+ra|n,rR} is an ideal of R that contains the element a. (This ideal is called the principal ideal of R that is generated by a. )15. Prove that if is an ideal in a commutative ring with unity, then is an ideal in .12. Let be a commutative ring with unity. If prove that is an ideal of.