57 288
Assignments Done
Successfully Done
In February 2018
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Algebra Question for Irvin

Question #16669
Let x, y be elements in a ring R such that Rx = Ry. Show that there exists a right R-module isomorphism f : xR → yR such that f(x) = y.
Expert's answer
Define f(xr) = yr for any r ∈ R. Note that if xr = xr', then x(r − r') = 0 implies that y(r − r') ∈ Rx(r − r') = 0.
This shows that yr = yr', so f is well-defined. Clearly, f is an R-module epimorphism from xR to yR, with f(x) = y. Finally, if xr ∈ ker(f), then yr = 0 and we have xr ∈ (Ry)r = 0. Therefore, f is the isomorphism we want.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!


No comments. Be first!

Leave a comment

Ask Your question