Скачать или смотреть Group Theory 2: Semigroup, Monoids and Inverses

We introduce the notion of a monoid and establish the law of exponents.

Timestamp provided by Vijay Kumar Sharma

[00:00:00] - Introduction
[00:02:57] - Defining Semigroup & Generalized Associativity
[00:08:08] - Identity Element Explained with Examples
[00:13:27] - Identity elements : Union & Intersection Cases
[00:15:00] - Example suggesting right but not left Identity.
[00:18:35] - From Semigroup to Monoid (Uniqueness of Identity Proof)
[00:23:00] - Defining a^n for nonnegative integers in a Monoid
[00:24:33] - Law of Exponents: a^(m+n) = a^m · a^n (Induction Proof)
[00:29:17] - Law of Exponents: (a^m)^n = a^(mn)
[00:33:33] - If a commutes with b then a commutes with b^n for non negative integer n. (Proof)
[00:38:40] - if a commutes with b then (a · b)^n = a^n · b^n for non negative integer n. (Proof)
[00:43:45] - Defining Inverses in Monoids with Examples
[00:53:00] - Uniqueness of Inverse & Preview of Next Lecture

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