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I am reading Paul E. Bland's book, "Rings and Their Modules".
I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand the proof of part of Proposition 4.2.14 ... ...
Proposition 4.2.14 reads as follows:
https://www.physicsforums.com/attachments/8237
https://www.physicsforums.com/attachments/8235
In the above proof by Bland we read the following:
"... ... Since $$M / M_1$$ is a simple R-module, $$M / M_1$$ is artinian and noetherian ... ... Can someone please explain why $$M / M_1$$ being a simple R-module implies that $$M / M_1$$ is artinian and noetherian ... ... ?Peter
I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand the proof of part of Proposition 4.2.14 ... ...
Proposition 4.2.14 reads as follows:
https://www.physicsforums.com/attachments/8237
https://www.physicsforums.com/attachments/8235
In the above proof by Bland we read the following:
"... ... Since $$M / M_1$$ is a simple R-module, $$M / M_1$$ is artinian and noetherian ... ... Can someone please explain why $$M / M_1$$ being a simple R-module implies that $$M / M_1$$ is artinian and noetherian ... ... ?Peter
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