Rectangular algebras

Algebras of the variety RA_τ generated by projection algebras (of type τ) are called rectangular algebras. It turns out that an algebra (A; F) is rectangular if and only if A can be decomposed in (i.e., encoded by) components in such a way that every term function f:Aⁿ→A can be performed in parallel and is a projection on each component (algebraically speaking, if <A; F> is isomorphic to a direct product of projection algebras). A list Σ_τ of identities that completely characterize rectangular algebras is given. Every term in RA_τ has a normal form. Some algorithms (for decomposition and normal form) and examples for finite algebras of finite type are given