A non-associative algebra is a mathematical structure that does not follow the associative property in multiplication. While this term is widely accepted, there are other words that can be used to describe a non-associative algebra. These include non-commutative algebra, alternative algebra, and Moufang loop. In non-commutative algebra, the order of multiplication matters, while in an alternative algebra, if the product of elements is zero, then at least one of the factors must be zero. A Moufang loop is an alternative algebra that satisfies a certain additional condition. Despite the varying terminology, all of these terms refer to a mathematical structure that does not follow the associative property in multiplication.