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I am reading Paul E. Bland's book, "Rings and Their Modules".
I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some help to fully understand the proof of part of Proposition 4.3.3 ... ...
Proposition 4.3.3 reads as follows:View attachment 8247
View attachment 8248
In the above proof by Bland we read the following:
"... ... If $$(d) = a_1 R + a_2 R + \ ... \ ... \ + a_n R$$, then each $$a_i$$ is in $$(d)$$ ... ... "Can someone please explain how $$(d) = a_1 R + a_2 R + \ ... \ ... \ + a_n R$$ implies each $$a_i$$ is in $$(d)$$ ... ..Peter
I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some help to fully understand the proof of part of Proposition 4.3.3 ... ...
Proposition 4.3.3 reads as follows:View attachment 8247
View attachment 8248
In the above proof by Bland we read the following:
"... ... If $$(d) = a_1 R + a_2 R + \ ... \ ... \ + a_n R$$, then each $$a_i$$ is in $$(d)$$ ... ... "Can someone please explain how $$(d) = a_1 R + a_2 R + \ ... \ ... \ + a_n R$$ implies each $$a_i$$ is in $$(d)$$ ... ..Peter