76 974
Assignments Done
98,5%
Successfully Done
In June 2019

Answer to Question #17650 in Abstract Algebra for Hym@n B@ss

Question #17650
Show that soc(M) ⊆ {m ∈ M : (rad R) • m = 0}, with equality if R/rad R is an artinian ring.
Expert's answer
The first conclusion follows fromthe fact that (rad R)V = 0 for any simple left R-module V. Now assume R/rad R is artinian. Let N = {m ∈ M : (rad R) · m = 0}, whichis an R-submodule of M. Viewing N as a module over thesemisimple ring R/rad R, we see that RN is semisimple.Therefore, N ⊆ soc(M), as desired.

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!

Comments

No comments. Be first!

Leave a comment

Ask Your question

Submit
Privacy policy Terms and Conditions