  A synaptic algebra is a common generalization of several ordered algebraic
structures based on algebras of self-adjoint operators, including the
self-adjoint part of an AW*-algebra. In this paper we prove that a synaptic
algebra A has the monotone square property, i.e., if a and b are positive
elements, then if a is less or equal than b, then the square root of a is less
or equal than the square root of b.
