Abstract Algebra, Lec 24A: Ring Definition, Ring Examples, Ring Basic Properties and Proofs

Abstract Algebra basic Ring Theory: Ring Definition, Ring Examples, Ring Basic Properties and their Proofs. "Contemporary Abstract Algebra", by Joe Gallian: https://amzn.to/2ZqLc1J Check out my blog at: https://infinityisreallybig.com/ Abstract Algebra Playlist: https://www.youtube.com/watch?v=lx3qJ-zjn5Y&list=PLmU0FIlJY-Mn3Pt-r5zQ_-Ar8mAnBZTf2 (0:00) Lecture plan and plan for the rest of the semester. (1:43) Review definition of a ring. (7:23) Our main emphasis in our study of rings: factorization, especially in polynomial rings. Definition of "divides" and an example in Z5[x]. (13:06) Review initial examples of rings, including rings of integers, the ring Zn, rings of matrices, the Gaussian integers, and the rationals with the square root of 2 adjoined. (26:37) Basic properties with simple (but somewhat tricky) proofs. AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.