Share
Explore BrainMass

Rings and Modules : Quasi-Regular and Module Homomorphisms

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.

Attachments

Solution Summary

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.

$2.19