The Ultimate Algebraic Structure

Abstract Algebra · Axiom Academy

INTRO Fields: The Ultimate Algebraic Structure Discover why fields sit atop the hierarchy of algebraic structures, possessing all the most desirable properties. Climbing the Algebraic Hierarchy Algebraic structures form a pyramid, with each level adding more structure and properties. Click on each level to explore what makes it special! In a field, every non-zero element has a multiplicative inverse. Compare this property in different structures! Click an element to test for inverse Fields inherit the "no zero divisors" property from integral domains. This means if a·b = 0, then either a = 0 or b = 0. Test this in different structures! One of the most powerful properties: any field naturally forms a vector space over any of its subfields!

This is the written version of the interactive lesson above. See the full Abstract Algebra course.