I am reading Paul E. Bland's book, "Rings and Their Modules".(adsbygoogle = window.adsbygoogle || []).push({});

I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand the proof of part of Proposition 4.2.4 ... ...

Proposition 4.2.4 reads as follows:

I need help to fully understand Part of the proof proving that ##(2) \Longrightarrow (3)## ...

In that part of the proof Bland seems to be assuming that

## \bigcap_F M_\alpha = N ##

if and only if

## \bigcap_F (M_\alpha / N ) = 0 ##

In other words, if ##F = \{ 1, 2, 3 \}## then

##M_1 \cap M_2 \cap M_3##

if and only if

##M_1 / N \cap M_2 / N \cap M_3 / N##

But whyis this the case ... ...exactly

... ... how do we formally and rigorously demonstrate that this is true ...

Hope someone can help ...

Peter

====================================================

Proposition 4.2.4 refers to the (possibly not well known) concept of cogeneration so I am providing Section 4.1 Generating as Cogenerating Classes ... ... as follows ...

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Artinian Modules - Bland - Proposition 4.24

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**