Projection algebras and rectangular algebras. (English) Zbl 0788.08007

Denecke, K. (ed.) et al., General algebra and applications. Based on lectures given at the 43. Arbeitstagung Allgemeine Algebra, Potsdam (Germany), 31. Jan. - 2. Febr. 1992. Berlin: Heldermann Verlag. Res. Expo. Math. 20, 180-194 (1993).
Projection algebras have as fundamental operations projection operations only. Rectangular algebras are algebras from the variety \(RA_ \tau\) generated by projection algebras (of type \(\tau\)). A basis of identities and a normal form of terms is presented for \(RA_ \tau\). An algebra is rectangular iff it is isomorphic to a direct product of projection algebras. The only subdirectly irreducible rectangular algebras are two- element projection algebras. The variety \(RA_ \tau\) is the least solid (i.e. characterized by hyperidentities) nontrivial variety in the lattice of all varieties of type \(\tau\). Algorithms for finding normal form of terms and decomposition of a rectangular algebra into a direct product of two-element projection algebras are given.
For the entire collection see [Zbl 0773.00016].
Reviewer: J.Henno (Tallinn)


08B26 Subdirect products and subdirect irreducibility
08B15 Lattices of varieties
08A40 Operations and polynomials in algebraic structures, primal algebras
20M07 Varieties and pseudovarieties of semigroups
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)