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: