I am reading Anderson and Feil - A First Course in Abstract Algebra.(adsbygoogle = window.adsbygoogle || []).push({});

I am currently focused on Ch. 8: Integral Domains and Fields ...

I need some help with an aspect of the proof of Theorem 8.7 (Fermat's Little Theorem) ...

Theorem 8.7 and its proof read as follows:

My questions regarding the above are as follows:

Question 1

In the above text from Anderson and Feil we read the following:

" ... ... Because a field has no zero divisors, each element of ##S## is non-zero ... "

Can someone please demonstrate exactly why this follows ... ?

Question 2

In the above text from Anderson and Feil we read the following:

" ... ... Because a field satisfies multiplicative cancellation, no two of these elements are the same .. ... "

Can someone please demonstrate exactly why it follows that no two of the elements of ##S## are the same .. ... "

Help will be appreciated ...

Peter

*** EDIT ***

oh dear ... can see that the answer to Question 1 is obvious ... indeed it follows from the definition of zero divisor .... apologies ... brain not in gear ...

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# I Fermat's Little Theorem ... Anderson and Feil, Theorem 8.7 .

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