| Title:
|
On Semi-Boolean-Like Algebras (English) |
| Author:
|
Ledda, Antonio |
| Author:
|
Paoli, Francesco |
| Author:
|
Salibra, Antonino |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
101-120 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Boolean-like algebra |
| Keyword:
|
central element |
| Keyword:
|
noncommutative lattice theory |
| MSC:
|
03C05 |
| MSC:
|
06E75 |
| idZBL:
|
Zbl 06285758 |
| idMR:
|
MR3202753 |
| . |
| Date available:
|
2013-08-02T08:02:01Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143395 |
| . |
| Reference:
|
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