- #1

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I am reading T. S. Blyth's book: Module Theory: An Approach to Linear Algebra ...

I am focused on Chapter 2: Submodules; intersections and sums ... and need help with the proof of Theorem 2.3 ...

Theorem 2.3 reads as follows:

In the above proof we read the following:

" ... ... A linear combination of elements of ##\bigcup_{ i \in I }## is precisely a sum of the form ##\sum_{ j \in J } m_j## for some ##J \in P(I)##. ... ... "

But ... Blyth defines a linear combination as in the text below ...

So ... given the above definition wouldn't a linear combination of elements of ##\bigcup_{ i \in I } M_i## be a sum of the form ##\sum_{ j \in J } \lambda_j m_j## ... and not just ##\sum_{ j \in J } m_j## ... ... ?

Hope someone can help ...

Peter

I am focused on Chapter 2: Submodules; intersections and sums ... and need help with the proof of Theorem 2.3 ...

Theorem 2.3 reads as follows:

In the above proof we read the following:

" ... ... A linear combination of elements of ##\bigcup_{ i \in I }## is precisely a sum of the form ##\sum_{ j \in J } m_j## for some ##J \in P(I)##. ... ... "

But ... Blyth defines a linear combination as in the text below ...

So ... given the above definition wouldn't a linear combination of elements of ##\bigcup_{ i \in I } M_i## be a sum of the form ##\sum_{ j \in J } \lambda_j m_j## ... and not just ##\sum_{ j \in J } m_j## ... ... ?

Hope someone can help ...

Peter