Abstract Algebra II: introduction to modules, 3-1-17

We're in Dummit and Foote's 3rd edition, Part III

[ClumpypooCP]

SO GLAD you have videos about modules!!

[adamrichard]

(21:07) Can you help me understand why we need the annihilator condition am=0 in order to make M into an (R/I)-module. Checking the axioms using the action (r+I)m=rm on R/I x M --> M, I did not seem to need the condition am=0. Hence, I suspect I missed something important. Thanks in advance.

[samsualam]

If 0 is a identity with an addition operation, 0 in R if we operate with an element m of M, is that true that 0r m = 0m?

[GopinathShanmugam]

sir which book you are preferring for module theory?