I am reading Abstract Algebra: Structures and Applications" by Stephen Lovett ...(adsbygoogle = window.adsbygoogle || []).push({});

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

I need help with the proof of, or at least some remarks concerning, Proposition 7.1.3 ...

Proposition 7.1.3 plus some introductory remarks (proof?) reads as follows:

In the above text from Lovett we read the following:

"... ... However, the multiplication on these elements as defined by distributivity gives this set of elements the structure of ##\mathbb{F}_p = \mathbb{Z} / p \mathbb{Z}##. ... ... "

... ... BUT ... the subfield contains elements ##0, 1, 2, 3, 4, 5, \ ... \ ... \ (p -1)##

... and being a field, it contains divisions of these elements such as ##1/2, 3/5 \ ... \ ... \ ...##

... so how can this subfield be equal to ##\mathbb{Z} / p \mathbb{Z}## ... ... ?

Hope someone can help ...

Peter

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Prime Subfiellds - Lovett, Proposition 7.1.3 ...

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**