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Abstract Algebra

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Moderate

Properties of Quotient Rings: Preservation of Properties

ABSALG-AHNL8W

Let $R$ be a ring and let $I \subseteq R$ be a (two-sided) ideal.

Which properties are preserved under taking the quotient $R/I$?

Select ALL that apply.

A

If $R$ is commutative, then $R/I$ is commutative.

B

If $R/I$ is commutative, then $R$ is commutative.

C

If $R$ contains no nontrivial zero divisors, then $R/I$ contains no nontrivial zero divisors.

D

If $R/I$ contains no nontrivial zero divisors, then $R$ contains no nontrivial zero divisors.

E

If $R$ is finite, then $R/I$ is finite.