On semi-Boolean-like algebras

LEDDA, ANTONIO;PAOLI, FRANCESCO;Salibra, A.

2013-01-01

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Abstract

In a previous paper, we introduced the notion of Boolean-like algebra as a generalisation of Boolean algebras to an arbitrary similarity type. In a nutshell, a double-pointed algebra A with constants 0,1 is Booolean-like in case for all a ∈ A the congruences θ (a,0) and θ (a,1) are compementary factor congruences of A. We also introduced the weaker notion of semi-Boolean-like algebra, showing that it retained some of the strong algebraic properties characterising Boolean algebras. In this paper, we continue the investigation of semi-Boolean like algebras. In particular, we show that every idempotent semi-Boolean-like variety is term equivalent to a variety of noncommutative Boolean algebras with additional regular operations.