On Semi-Boolean-Like Algebras

Ledda, Antonio, Paoli, Francesco, and Salibra, Antonino. "On Semi-Boolean-Like Algebras." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 52.1 (2013): 101-120. <http://eudml.org/doc/260653>.

@article{Ledda2013,
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 $\mathbf \{A\}$ with constants $0,1$ is Boolean-like in case for all $a\in A$ the congruences $\theta \left( a,0\right) $ and $\theta \left( a,1\right) $ are complementary factor congruences of $\mathbf \{A\}$. 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.},
author = {Ledda, Antonio, Paoli, Francesco, Salibra, Antonino},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Boolean-like algebra; central element; noncommutative lattice theory; Boolean-like algebras; semi-Boolean-like algebras; central elements; noncommutative lattice theory; varieties of noncommutative Boolean algebras},
language = {eng},
number = {1},
pages = {101-120},
publisher = {Palacký University Olomouc},
title = {On Semi-Boolean-Like Algebras},
url = {http://eudml.org/doc/260653},
volume = {52},
year = {2013},
}

TY - JOUR
AU - Ledda, Antonio
AU - Paoli, Francesco
AU - Salibra, Antonino
TI - On Semi-Boolean-Like Algebras
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2013
PB - Palacký University Olomouc
VL - 52
IS - 1
SP - 101
EP - 120
AB - 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 $\mathbf {A}$ with constants $0,1$ is Boolean-like in case for all $a\in A$ the congruences $\theta \left( a,0\right) $ and $\theta \left( a,1\right) $ are complementary factor congruences of $\mathbf {A}$. 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.
LA - eng
KW - Boolean-like algebra; central element; noncommutative lattice theory; Boolean-like algebras; semi-Boolean-like algebras; central elements; noncommutative lattice theory; varieties of noncommutative Boolean algebras
UR - http://eudml.org/doc/260653
ER -