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MMLU / Let R be a ring with a multiplicative identity. If U is an additive subgroup of…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Let R be a ring with a multiplicative identity. If U is an additive subgroup of R such that ur in U for all u in U and for all r in R, then U is said to be a right ideal of R. If R has exactly two right ideals, which of the following must be true?
I. R is commutative.
II. R is a division ring (that is, all elements except the additive identity have multiplicative inverses).
III. R is infinite.

choices

  1. I only
  2. II only
  3. III only
  4. I and II only

subject

college_mathematics

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Source and history

task_id
5ee9858f-e2ee-563f-9b13-2a27a67d180b
task_key
all--test--5ee9858f-e2ee-563f-9b13-2a27a67d180b
task_revision_id
1
config / split
all / test

Official source

initial import