Definition:Self Distributive

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

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

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

Also defined as

The term is sometimes used for operations for which only one of the above holds.

Also see