Let R be a ring such that the only right ideals of R are (0) and R.
Prove that either R is a division ring
or, that R is a ring with a prime number of elements in which ab = 0 for
every a,b Є R.
Please see the attached file for the complete solution.
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Ring Theory (V)
Ideals of a Ring
By:- Thokchom Sarojkumar Sinha
Let be a ring such that the only right ideals of are and . Prove that either is a division ring
or, that is a ring with a prime number of elements in which for every
Solution:- Suppose that is in .
Consider the set .
We have to show that is a right ideal of .
Let then ,
Division rings are investigated. The solution is detailed and well presented.