Question

If u andv are units, prove that u and v are associates.

Short answer

It has been provedthat u and v are associates.

Step-by-step solution

Given that

Given that u and v are units in an integral Domain R.

Prove that u and v are associates

Note that u can be written as

$u=v\left(v^{-1}u\right)$and clearly $v^{-1}u$is a unit as $v^{-1}$and uare units.

Thus, u is associate of v.

Also, v is associate of u.

Conclusion

Thus it can be concluded that if u andv are units then u and v are associates.