Definition:Left Distributive

Definition

Let $S$ be a set on which is defined two binary operations, defined on all the elements of $S \times S$, which we will denote as $\circ$ and $*$.

The operation $\circ$ is left distributive over the operation $*$ iff:

$\forall a, b, c \in S: a \circ \left({b * c}\right) = \left({a \circ b}\right) * \left({a \circ c}\right)$

Also see

• Right Distributive
• Distributive

Sources

• W.E. Deskins: Abstract Algebra (1964): Exercise $1.4: 6$
• Seth Warner: Modern Algebra (1965)... (previous)... (next): Exercise $16.23$
• B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra (1970): $\S 1.1$: Definitions $1.1 \ \text{(c)}$