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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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    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.

    $2.49

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