Skew Boolean algebras (SBA) and Boolean-like algebras (nBA) are one-pointed and n-pointed noncommutative generalisation of Boolean algebras, respectively. We show that any nBA is a cluster of n isomorphic right-handed SBAs, axiomatised here as the variety of skew star algebras. The variety of skew star algebras is shown to be term equivalent to the variety of nBAs. We use SBAs in order to develop a general theory of multideals for nBAs. We also provide a representation theorem for right-handed SBAs in terms of nBAs of n-partitions.
Antonino Salibra (Corresponding)
|Data di pubblicazione:||2019|
|Titolo:||On Noncommutative Generalisations of Boolean Algebras|
|Rivista:||THE ART OF DISCRETE AND APPLIED MATHEMATICS|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.26493/2590-9770.1323.ceb|
|Appare nelle tipologie:||2.1 Articolo su rivista |