Abstract Algebra 73: Two equivalent definitions of fields - one condensed, one expanded

Abstract Algebra 73: Two equivalent definitions of fields - one condensed, one expanded

Abstract: We give two equivalent definitions of fields. One definition is efficient and condensed, whereas the other definition is longer and more explicit. Students who are learning about fields for the first time often prefer the more explicit definition. We comment on how these two definitions are equivalent to each other.

This video accompanies the class "Introduction to Abstract Algebra" at Colorado State University:

[gfjzlis]

Hi Henry! Is the distributivity proved by the other basic axioms or on its own?