Summary: Rings and Algebras Problem set #9: Solutions Nov. 17, 2011.
1. a) Let I be a right ideal in a ring R. Show that for any R-module M we have R/I
R
M
M/IM as Abelian groups.
b) Compute Zm
Z
Zn.
Solution. a) Take the exact sequence of right R-modules 0 I R R/I 0 and tensor it with
M. We get the following exact sequence (for the proof of right exactness we refer to Problem #9/3):
I
R
M R
R
M R/I
R
M 0. Here the image of I
R
M in R
R

Source: Ágoston, István - Institute of Mathematics, Eötvös Loránd University

Collections: Mathematics