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I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ...

I am currently focused on Chapter 7: Field Extensions ... ...

I need help with some remarks of Lovett following Theorem 7.1.12 and Example 7.1.13 on page 326 ...

The remarks by Lovett read as follows:

In the above remarks from Lovett, we read the following:

" ... ... In the quotient ring ##K##, this implies that ##\overline{ a(x) q(x) } = 1##. Thus in ##K, \ a( \alpha ) q( \alpha ) = 1##. ... ... "

My question is as follows:

Can someone please explain exactly why/how it is that ##\overline{ a(x) q(x) } = 1## implies that ##a( \alpha ) q( \alpha ) = 1## ... ... ?

Help will be appreciated ...

Peter

I am currently focused on Chapter 7: Field Extensions ... ...

I need help with some remarks of Lovett following Theorem 7.1.12 and Example 7.1.13 on page 326 ...

The remarks by Lovett read as follows:

In the above remarks from Lovett, we read the following:

" ... ... In the quotient ring ##K##, this implies that ##\overline{ a(x) q(x) } = 1##. Thus in ##K, \ a( \alpha ) q( \alpha ) = 1##. ... ... "

My question is as follows:

Can someone please explain exactly why/how it is that ##\overline{ a(x) q(x) } = 1## implies that ##a( \alpha ) q( \alpha ) = 1## ... ... ?

Help will be appreciated ...

Peter