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

I am focused on Section 6.1 The Jacobson Radical ... ...

I need help with the proof of Proposition 6.1.7 ...Proposition 6.1.7 and its proof read as follows:

In the above text from Bland, in the proof of (1) we read the following:

" ... ... Since ##S## is a simple ##R##-module if and only if there is a maximal ideal ##\mathfrak{m}## of ##R## such that ##R / \mathfrak{m} \cong S## ... ... "I do not follow exactly why the above statement is true ...

Can someone help me to see why and how, exactly, the above statement is true ...

Hope someone can help ...

Peter

I am focused on Section 6.1 The Jacobson Radical ... ...

I need help with the proof of Proposition 6.1.7 ...Proposition 6.1.7 and its proof read as follows:

In the above text from Bland, in the proof of (1) we read the following:

" ... ... Since ##S## is a simple ##R##-module if and only if there is a maximal ideal ##\mathfrak{m}## of ##R## such that ##R / \mathfrak{m} \cong S## ... ... "I do not follow exactly why the above statement is true ...

Can someone help me to see why and how, exactly, the above statement is true ...

Hope someone can help ...

Peter