1. Let R be a ring. Prove that if x, y E R such that xy is right quasi-regular then yx is also right quasi-regular.
3. Let M and N be left R-modules. Let f : M N and g : N M be left R-module homomorphisms such that fg(y) = y for all y N. Show that M = ker(f) im(g).
Please see attached.© BrainMass Inc. brainmass.com December 24, 2021, 5:17 pm ad1c9bdddf
Please see the attached file for the full solution.
Thanks for using BrainMass.
We know, is right quasi-regular in a ring if and only if is right invertible. i.e. there exists some , such that .
Now for any , if is right quasi-regular, then there exists , such that ...
Quasi-regular elements of a ring, module homomorphisms and kernels are investigated. The solution is detailed and well presented. The response was given a rating of "5" by the student who originally posted the question.