1. Perfect extensions of de Morgan algebras
| Title | Perfect extensions of de Morgan algebras |
|---|---|
| Author info | Miroslav Haviar, Miroslav Ploščica |
| Author | Haviar Miroslav 1965- (50%) UMBFP10 - Katedra matematiky |
| Co-authors | Ploščica Miroslav (50%) |
| Source document | Algebra Universalis. Vol. 82, no. 4 (2021), art. no. 58, pp. 1-8. - Basel : Springer Nature Switzerland AG, 2021 |
| Keywords | De Morganova algebra - De Morgan algebra MS-algebra rozšírenie - extension Boolean algebra |
| Form. Descr. | články - journal articles |
| Language | English |
| Country | Switzerland |
| Annotation | An algebra A is called a perfect extension of its subalgebra B if every congruence of B has a unique extension to A. This terminology was used by Blyth and Varlet [1994]. In the case of lattices, this concept was described by Grätzer and Wehrung [1999] by saying that A is a congruence-preserving extension of B. Not many investigations of this concept have been carried out so far. The present authors in another recent study faced the question of when a de Morgan algebra M is perfect extension of its Boolean subalgebra B(M), the so-called skeleton of M. In this note a full solution to this interesting problem is given. The theory of natural dualities in the sense of Davey and Werner [1983] and Clark and Davey [1998], as well as Boolean product representations, are used as the main tools to obtain the solution. |
| URL | Link na plný text Link na zdrojový dokument |
| Public work category | ADC |
| No. of Archival Copy | 50558 |
| Catal.org. | BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici |
| Database | xpca - PUBLIKAČNÁ ČINNOSŤ |
| References | PERIODIKÁ-Súborný záznam periodika |