# Ring Theory : Division Rings

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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.

https://brainmass.com/math/ring-theory/ring-theory-division-rings-97572

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Modern Algebra

Ring Theory (V)

Ideals of a Ring

Division 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 ,

...

#### Solution Summary

Division rings are investigated. The solution is detailed and well presented.

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