Definition:Self-Distributive Operation/Left

Definition

Let $\circ$ be a binary operation on the set $S$.

$\circ$ is left self-distributive if and only if:

$\forall a, b, c \in S: a \circ \paren {b \circ c} = \paren {a \circ b} \circ \paren {a \circ c}$

Also known as

Some sources use the term left distributive over itself

Also see

• Definition:Right Self-Distributive Operation

• Results about self-distributive operations can be found here.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 16$: The Natural Numbers: Exercise $16.23 \ \text{(c)}$