求math practice book 上的第六十六题

nickmars77UID: 2399318

66. let R be a ring with a multiplicative identity. if U is an additive subgroup of R such that ur属于U for all u属于U and for all r属于R， then U is said to be aright ideal of R. if R has exactly two right ideals, which of the following must be true?

2. R is a division ring.

求证明过程啊

gbbrianUID: 2322155

You only have to show every element r in R has an inverse. By contradiction, for if there exists a r that has no inverse, then the ring generated by r <r> is an non-trivial right ideal, which is a contradiction.
Best wishes for your tomorrow! hehe