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Euclidean Rings and GCD

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.