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I am reading Dummit and Foote's book: "Abstract Algebra" (Third Edition) ...
I am currently studying Chapter 10: Introduction to Module Theory ... ...
I need some help with an aspect of Example (5) of Section 10.1 Basic Definitions and Examples ... ... Example (5) reads as follows:
View attachment 7999
View attachment 8000
I do not fully understand this example and hence need someone to demonstrate (explicitly and completely) why it is necessary for $$am = 0$$ for all $$a \in I$$ and all $$m \in M$$ for us to be able to make $$M$$ into an $$(R/I)$$-module. ...
Help will be much appreciated ..
Peter
I am currently studying Chapter 10: Introduction to Module Theory ... ...
I need some help with an aspect of Example (5) of Section 10.1 Basic Definitions and Examples ... ... Example (5) reads as follows:
View attachment 7999
View attachment 8000
I do not fully understand this example and hence need someone to demonstrate (explicitly and completely) why it is necessary for $$am = 0$$ for all $$a \in I$$ and all $$m \in M$$ for us to be able to make $$M$$ into an $$(R/I)$$-module. ...
Help will be much appreciated ..
Peter