Abstract Alg, Lec 25A: Ring Integral Domains, Fields, Ring Characteristic, Nilpotents & Idempotents

Abstract Algebra definitions from ring theory of integral domain, field, and ring characteristic. Also discuss nilpotent and idempotent elements and examples. "Contemporary Abstract Algebra", by Joe Gallian: https://amzn.to/2ZqLc1J. Check out my blog at: https://infinityisreallybig.com/. Abstract Algebra Playlist:    • Abstract Algebra Course, Lecture 1: Introd...  

Abstract Algebra, Lecture 25A.

(0:00) The Great Tau-Shaped Superstorm of April 2018.
(4:08) Lecture summary (make sure you study more complicated examples before Lecture 26).
(5:57) Review the idea of the group of units of a commutative ring and examples.
(9:03) Review definition of zero-divisor (consider an example of finding solutions of a polynomial equation in different rings), integral domain (no zero-divisors, so multiplicative cancellation law holds), field, basic examples and properties.
(21:21) Characteristic of a ring and basic theorems.
(27:33) Nilpotent and idempotent elements in a ring and basic examples and facts.

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