Abstract Algebra 71: An introduction to fields

IMPORTANT: At 0:25 I misspoke and said something clearly false. I meant to say every field is a ring, but not every ring is a field!

Abstract Algebra 71: An introduction to fields

Abstract: We give an introduction to fields. These are algebraic structures which have two binary operations, addition and multiplication. The field is an abelian group under addition, and an abelian group under multiplication once zero (the additive identity) is removed. Examples include the real numbers, the rationals, the complex numbers, and Z/pZ for p prime.

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

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It is interesting, people often think there are 4 basic operations in arithmetic. In fact, there are really two, since subtraction is addition with negatives and division is multiplication by inverses.

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0:25 every field is a ring but not vice a versa (not every ring is a field).