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    Euclidean Rings and GCD

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    If the least common multiple of a and b in the Euclidean ring R is denoted by [a,b],
    prove that
    [a,b] = ab/(a, b) where (a, b) is the greatest common divisor of a and b.

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    Modern Algebra
    Ring Theory (XVIII)
    Euclidean Ring
    Greatest Common Divisor
    Least Common Multiple

    By:- Thokchom Sarojkumar Sinha

    If the least common multiple of and in the Euclidean ring is denoted by ,

    Solution Summary

    Euclidean Rings and GCD are investigated. The solution is detailed and well presented.