TSSFL TECHNOLOGY STACK

We start with important points that we believe will help anyone to learn, not only abstract algebra but mathematics in general:

Understand...

Isomorphism is a map between two groups, which is a bijection (one-to-one and onto) such that $f:G \rightarrow G'$. E.g., $f(x,y) = f(x)f(y)$ gives...

This video series is an exploration of the theoretical foundations of abstract algebra needed to understand the nature of solutions to polynomial...

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between...

Find out rotation about the center which maps equilateral triangle to itself.

Problem

Prove by induction on n that 3 always divides n^3 - n .

Proof

3 divides n^3 - n \implies \frac{n^3 - n}{3} = m, \implies n^3-n = 3m, \...

A subgroup N of a group G is said to be a normal subgroup of G if gng^{-1} \in N for all
n\in N and g\in G .

We use the notation N\triangle G to...

This is an example of how you can apply left and right cancellation to solve a group related problem in abstract algebra.

Let G be a group, and...

H is a subgroup of a group G if the identity element belongs to H ; a, b \in H \implies \ ab\in H and also the inverse element belongs to H . We...

To prove that a binary operation on a certain set, say G makes it a group, we need to show that four properties are satisfied. Let's illustrate this...

A group is an algebraic structure that is closed under binary operation, associative, each of its element has an inverse and there is a common...

In mathematics, congruence modulo n (referred to as well modular arithmetic) is a system of arithmetic for integers, where numbers wrap around upon...

We provide these examples to help you get started.

Problem 1. Let G be a group, a, \ b \in G such that a^5 = e, \ b \ne e, \ b^2 = aba^{-1} . Find...

Problem: Let G be a group. Suppose that (ab)^2 = a^2b^2 , \ \ \forall \ a, \ b \in G , prove that G is abelian.

Proof
(ab)^{2}(ab)^{-1} =...

The Euclidean Algorithm uses the Division Algorithm repeatedly to find the greatest common divisor (gcd) of two numbers.

Division Algorithm states...

Here are the problems. They will teach you how to prove mathematical statements by using induction method.

Problem 1

Let a, b \in G such that ab =...

We explore a couple of examples that involve relatively prime integers and greatest common divisor (gcd).

We will make use of the following fact:...

Download A First Course in Abstract Algebra Book from

Qn. Show that the intersection of two ideals of a ring R is an ideal