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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.

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

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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 provided by:
  • BSc, Manipur University
  • MSc, Kanpur University
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