## Field Generated by 1

We find the smallest field containing the number 1 when using the usual addition and multiplication of real numbers.

## Integral Domain of Integers

We show that the integers modulo any prime forms an integral domain under addition and multiplication modulo p.

## A Ring of Matrices

We show, step-by-step, that the set of all 2 x 2 matrices with real entries forms a ring under addition and multiplication.

## A Ring of Mappings

We show that the set of all mapping of real numbers with the operations of sums and products forms a commutative ring with identity.