# Non-associative ring

From Groupprops

## Definition

A **non-associative ring**, more properly called a **possibly non-associative ring** or a *not necessarily associative ring*, is defined as a set equipped with the following operations:

- An infix binary operation , called
*addition*. - A prefix unary operation , called the
*negative*. - A constant element , called
*zero*. - A binary operation , called the
*multiplication*.

satisfying the following compatibility conditions:

- forms an abelian group with group operation , inverse operation , and identity element .
- satisfies the two distributivity laws:
- Associativity: