Rectangular algebras

Abstract

Algebras of the variety RA/sub tau / generated by projection algebras (of type tau ) 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:A/sup n/ to A can be performed in parallel and is a projection on each component (algebraically speaking, if is isomorphic to a direct product of projection algebras). A list Sigma /sub tau / of identities that completely characterize rectangular algebras is given. Every term in RA/sub tau / has a normal form. Some algorithms (for decomposition and normal form) and examples for finite algebras of finite type are given.<>