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I am reading Anderson and Feil - A First Course in Abstract Algebra.

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:

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 ... ?

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

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 ...

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:

**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 ...