Robbins Algebra

In abstract algebra, a Robbins algebra is an algebra containing a single binary operation, usually denoted by, and a single unary operation usually denoted by . These operations satisfy the following axioms:

For all elements a, b, and c:

  1. Associativity:
  2. Commutativity:
  3. Robbins equation:

For many years, it was conjectured, but unproven, that all Robbins algebras are Boolean algebras. This was proved in 1996, so the term "Robbins algebra" is now simply a synonym for "Boolean algebra".

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