Definition:Non-Associative Ring with Unity

Definition
A non-associative ring with unity is a non-associative ring $(R, +, \times)$ such that $(R, \times)$ is a unitary magma.

Also see

 * Definition:Unital Algebra

Weaker properties

 * Definition:Ringoid
 * Definition:Non-Associative Semiring
 * Definition:Non-Associative Ring

Stronger properties

 * Definition:Ring with Unity
 * Definition:Commutative Ring with Unity