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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 Rmodule M we have
 

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 R­module M we have
R/I# R
M #
M/IM as Abelian groups.
b) Compute
Zm# Z
Z n .
Solution. a) Take the exact sequence of right R­modules 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
M is generated by elements of the

  

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

 

Collections: Mathematics