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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 
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Title Congruence pairs of principal MS-algebras and perfect extensions Author info Abd El-Mohsen Badawy, Miroslav Haviar, Miroslav Ploščica Author El-Mohsen Badawy Abd (34%)
Co-authors Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Ploščica Miroslav (33%)
Source document Mathematica Slovaca. Vol. 70, no. 6 (2020), pp. 1275-1288. - Bratislava : Slovenská akadémia vied, Matematický ústav SAV, 2020 Keywords algebra - algebra MS-algebra MS-kongruenčné dvojice - MS-congruence pairs Form. Descr. články - journal articles Language English Country Slovak Republic Annotation V práci je študovaný pojem kongruenčnej dvojice pre hlavné MS-algebry, ktorý je jednoduchší než pojem zavedený Beazerom pre K2-algebry. Je dokázané, že kongruencie hlavných MS-algebier L korešpondujú s MS-kongruenčnými dvojicami na jednoduchších podštruktúrach asociovaných k L. Analógia so známym Grätzerovým problémom formulovaným pre distributívne p-algebry je prezentovaná pre hlavné MS-algebry (Problém 1). V práci je demonštrované na triede hlavných MS-algebier, že možné riešenie problému môže byť jednoduché a elegantné. Ako krok k opisnejšiemu riešeniu Problému 1 je následne uvažovaný špeciálny prípad, keď hlavná MS-algebra L je perfektným rozšírením jej najväčšej Stoneovej podalgebry LS. Dva príklady ilustrujúce kedy tento špeciálny prípad nastáva a kedy nie sú prezentované. / The notion of a congruence pair for principal MS-algebras, simpler than the one given by Beazer for K2-algebras, is studied. It is proved that the congruences of the principal MS-algebras L correspond to the MS-congruence pairs on simpler substructures associated to L. An analogy of a well-known Grätzer’s problem formulated for distributive palgebras is presented here for the principal MS-algebras (Problem 1). It is demonstrated here on the class of principal MS-algebras that a possible solution to the problem can be simple and elegant. As a step to a more descriptive solution of Problem 1, a special case is then considered when a principal MS-algebra L is a perfect extension of its greatest Stone subalgebra LS. Two examples illustrating when this special case happens and when it does not are presented URL Link na plný text Public work category ADN No. of Archival Copy 49000 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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Title Triple construction of decomposable MS-algebras Author info Abd El-Mohsen Badawy, Daniela Guffová, Miroslav Haviar Author El-Mohsen Badawy Abd (34%)
Co-authors Guffová Daniela 1987- (33%) UMBFP10 - Katedra matematiky
Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Source document Mathematica : Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium. Vol. 51, no. 2 (2012), pp. 53-65. - Olomouc : Universita Palackého, 2012 Keywords MS-algebra principal MS-triple de Morgan algebra Language English Country Czech Republic systematics 512 Public work category ADE No. of Archival Copy 23420 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ article
Title On a certain construction of MS-algebras Author info Miroslav Haviar Author Haviar Miroslav 1965- (100%) UMBPF03 - Katedra matematiky
Source document Portugaliae Mathematica. Vol. 51, no. 1 (1994), pp. 71-83. - Zürich : European Mathematical Society Publishing House, 1994 Keywords algebra - algebra teória zväzov MS-algebra štúdie Language English Country Germany systematics 512 Public work category ADE Repercussion category GRAMAGLIA, Hector. On a certain construction of lattice expansions. In Mathematica Bohemica. ISSN 0862-7959, vol. 129, no. 1 (2004), pp. 1-9.
BADAWY, Abd El-Mohsen. On a construction of modular GMS-algebras. In Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium : mathematica. ISSN 0231-9721, 2015, vol. 54, no. 1, pp. 19-31.
Catal.org. UKUMB###BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ unrecognised