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I am reading Paul E. Bland's book "Rings and Their Modules" ...

Currently I am focused on Section 4.2 Noetherian and Artinian Modules ... ...

I need some help in order to fully understand Example 3, Section 4.2 ...

Example 3, Section 4.2 reads as follows:

My questions are as follows:

Can someone please explain/illustrate the nature of ##V_1## ... ?

Can someone please demonstrate exactly how ##V_1 \subseteq V_2 \subseteq V_3 \subseteq## ...

Help will be appreciated ...

Peter

Currently I am focused on Section 4.2 Noetherian and Artinian Modules ... ...

I need some help in order to fully understand Example 3, Section 4.2 ...

Example 3, Section 4.2 reads as follows:

My questions are as follows:

**Question 1**Can someone please explain/illustrate the nature of ##V_1## ... ?

**Question 2**Can someone please demonstrate exactly how ##V_1 \subseteq V_2 \subseteq V_3 \subseteq## ...

Help will be appreciated ...

Peter