Geodesic
On Semi-Boolean-Like Algebras
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 1, pp. 101-120.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 03C05, 06E75
Keywords: Boolean-like algebra; central element; noncommutative lattice theory 
@article{AUPO_2013__52_1_a8,
     author = {Ledda, Antonio and Paoli, Francesco and Salibra, Antonino},
     title = {On {Semi-Boolean-Like} {Algebras}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {101--120},
     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {2013},
     mrnumber = {3202753},
     zbl = {06285758},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2013__52_1_a8/}
}
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
SP  - 101
EP  - 120
VL  - 52
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUPO_2013__52_1_a8/
LA  - en
ID  - AUPO_2013__52_1_a8
ER  - 
%0 Journal Article
%A Ledda, Antonio
%A Paoli, Francesco
%A Salibra, Antonino
%T On Semi-Boolean-Like Algebras
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2013
%P 101-120
%V 52
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUPO_2013__52_1_a8/
%G en
%F AUPO_2013__52_1_a8
Ledda, Antonio; Paoli, Francesco; Salibra, Antonino. On Semi-Boolean-Like Algebras. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 1, pp. 101-120. http://geodesic.mathdoc.fr/item/AUPO_2013__52_1_a8/