A friend of mine sat down with me yesterday and complained that concepts in abstract algebra have not been taught to him in an intuitive way. He also said that he could not find an intuitive explanation for what I am about to write ANYWHERE on the internet.

So I thought I would give it a crack.

This object is comprised of a set and an operator. It also has a condition, it needs to be closed.

This object is a magma that has an extra condition, it needs to be associative.

This object is a semigroup but has an extra condition, it needs to have identities.

This object is a monoid but has an extra condition, it needs to have inverses.

This object is a group but it has an extra condition, it needs to be commutative.

This object is comprised of a set and two operators. The set with the first operator must satisfy the conditions to be an abelian group. The set with the second operator must satisfy the conditions to be a monoid. It also has an extra condition, it needs to satisfy distributivity.

This object is a more strict version of a ring. It needs the condition that the set with the identity element for the first operator is removed forms an abelian group with the second operator.

A snapshot in the cover photo show this nicely.

More to come…