Explore BrainMass
Share

Ring Theory and Cartesian Product

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

If R and S are rings, the cartesian product RxS is a ring too with operations

(r1,s1) + (r2,s2) = (r1+r2,s1+s2)
(r1,s1)*(r2,s2) = (r1*r2,s1*s2)

identity elements
0RxS = (0R,0s) 1RxS = (1R,1S)

and additive inverse -(r,s) = (-r,-s)

If R and S are nontrivial rings, show that RxS has at least 4 idempotent elements

© BrainMass Inc. brainmass.com March 21, 2019, 8:56 pm ad1c9bdddf
https://brainmass.com/math/ring-theory/ring-theory-cartesian-product-354495

Solution Summary

Ring theory is clarified in this solution.

$2.19