I am reading T. S. Blyth's book "Module Theory: An Approach to Linear Algebra" ... ... and am currently focussed on Chapter 1: Modules, Vector Spaces and Algebras ... ...(adsbygoogle = window.adsbygoogle || []).push({});

I need help with an aspect of Theorem 1.1 part 4 ...

Theorem 1.1 in Blyth reads as follows:

In the above text, in part 4 of the Theorem we read:

" ... ... when ##R## is a division ring

(4) ##\lambda x = 0_M## implies ##\lambda = 0_R## or ##x = 0_M## ... ... "

Blyth proves that if ##R## is a division ring and ##\lambda x = 0_M## with ##\lambda \neq 0_R## then we have that ##x = 0_M## ... ...

But ... ... Blyth does not show that if ##R## is a division ring and ##\lambda x = 0_M## with ##x \neq 0_M## then we have that ##\lambda = 0_R## ... ...

Can someone please help me to prove this ...

Peter

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# I Module Over a Division Ring - Blyth Theorem 1.1, Part 4

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