# Ring theory proof

Modern Algebra

Ring Theory (VIII)

The Field of Quotients of an Integral Domain

Prove the distributive law in F , the field of quotients of D, where D is the ring of integers.

© BrainMass Inc. brainmass.com April 1, 2020, 1:00 pm ad1c9bdddfhttps://brainmass.com/math/ring-theory/ring-theory-proof-in-modern-algebra-98114

#### Solution Preview

see attached

Prove the distributive law in , the field of quotients of , where is the ring of integers.

Solution:- We have to prove that

-----------------------(1)

(Right distributive law)

-----------------------(2)

(Left distributive law)

L.H.S. of (1)

...

#### Solution Summary

This is a ring theory proof of the distributive law in the field of quotients of the ring of integers.