# Ring Theory: Euclidean Rings and Elements with Least Common Multiples

Given two elements a, b in the Euclidean ring R their least common multiple cЄR is an element in R such that a│c and b│c and such that whenever a│x and b│x for xЄR then c│x. Prove that any two elements in the Euclidean ring R have a least common multiple in R.

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Modern Algebra

Ring Theory (XVII)

Euclidean Ring

Least Common Multiple

By:- Thokchom Sarojkumar Sinha

Given two elements in the Euclidean ring their least ...

#### Solution Summary

Euclidean Rings and Elements with Least Common Multiples are investigated. The solution is detailed and well presented.

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