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Does in a commutative ring every ideal is maximal? - Answers

No. For instance in R, which is commutative, we have the ideals (2) and (4), where (4) is strictly contained in (2), which is not R. Therefore the ideal (4) is not a maximal ideal.



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Does in a commutative ring every ideal is maximal? - Answers

https://math.answers.com/math-and-arithmetic/Does_in_a_commutative_ring_every_ideal_is_maximal

No. For instance in R, which is commutative, we have the ideals (2) and (4), where (4) is strictly contained in (2), which is not R. Therefore the ideal (4) is not a maximal ideal.



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https://math.answers.com/math-and-arithmetic/Does_in_a_commutative_ring_every_ideal_is_maximal

Does in a commutative ring every ideal is maximal? - Answers

No. For instance in R, which is commutative, we have the ideals (2) and (4), where (4) is strictly contained in (2), which is not R. Therefore the ideal (4) is not a maximal ideal.

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      No. For instance in R, which is commutative, we have the ideals (2) and (4), where (4) is strictly contained in (2), which is not R. Therefore the ideal (4) is not a maximal ideal.

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