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

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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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thank you very much for these lectures! i am studying for my exam and these lectures are very helpful!! 🙂 I am glad i found them

laura-yfjb
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Hi sir, when we say binary operation "multiplication" in context of ring, does it also mean "closure ?"I am confused because a ring is not necessarily a group under multiplication.
Thanks

sherryj