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Title Factor principal congruences and Boolean products in filtral varieties Author info Brian A. Davey, Miroslav Haviar Author Davey Brian A. (50%)
Co-authors Haviar Miroslav 1965- (50%) UMBFP10 - Katedra matematiky
Source document Algebra Universalis. Vol. 85, no. 19 (2024), pp. 1-23. - Basel : Springer Nature Switzerland AG, 2024 Keywords algebra - algebra Boolean algebra kongruencie Form. Descr. články - journal articles Language English Country Switzerland Annotation Motivated by Haviar and Ploščica's 2021 characterisation of Boolean products of simple De Morgan algebras, we investigate Boolean products of simple algebras in filtral varieties. We provide two main theorems. The first yields Werner's Boolean-product representation of algebras in a discriminator variety as an immediate application. The second, which applies to algebras in which the top congruence is compact, yields a generalisation of the Haviar–Ploščcica result to semisimple varieties of Ockham algebras. The property of having factor principal congruences is fundamental to both theorems. While major parts of our general theorems can be derived from results in the literature, we offer new, self-contained and essentially elementary proofs. URL https://link.springer.com/article/10.1007/s00012-024-00846-8 Public work category ADC No. of Archival Copy 54297 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 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 article
Title Aplikácia Booleovej algebry v technike Par.title Application of Boolean algebra in technology Author info Daniel Novák, Veronika Klopanová Author Novák Daniel 1952- (50%) UMBFP07 - Katedra techniky a technológií
Co-authors Nováková Veronika 1992- (50%) UMBFP10 - Katedra matematiky
Source document Technika a vzdelávanie : časopis zameraný na technické vzdelávanie v základných, stredných, i na vysokých školách, na oblasť základného a aplikovaného výskumu, aplikáciu informačných technológií vo výučbe odborných predmetov. Roč. 5, č. 1 (2016), s. 35-38. - Banská Bystrica : Vydavateľstvo Univerzity Mateja Bela - Belianum, 2016 Keywords Booleova algebra výroky - statements logické funkcie a premenné logické obvody technická elektronika učebné pomôcky - teaching aids Boolean algebra propositions logic functions and variables logic circuits technical electronics Language Slovak Country Slovak Republic systematics 37 Annotation Štúdia sa zaoberá problematikou využitia algebry logiky v elektrických obvodoch. V nadväznosti na základnú charakteristiku Booleovej algebry a jej zákony sa venuje aktuálnemu stavu výučby učiva logických obvodov v slovenskom základnom školstve. Následne navrhuje sústavu úloh, slúžiacich na precvičenie tohto učiva v predmete technika. Záverom stručne zhŕňa aktuálny stav a odporúča ďalší postup. = The study deals with the use of logical algebra in electrical circuits. Following the basic characteristics of Boolean algebra and its laws, the study presents the current state of teaching of the matter Logical Circuits in Slovak primary education. Further it proposes a set of tasks used to practice this curriculum in the subject Technology. Finally, the paper briefly summarizes the current state and it recommends further actions. Public work category ADF No. of Archival Copy 37402 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ 
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File name Downloaded Size Comment 37402 22 1.1 MB Title Introduction to Boolean algebras Author info Steven Givant, Paul Halmos Author Givant Steven
Co-authors Halmos Paul R.
Issue data New York, USA : Springer , c2009. - 574 s. : il., tab., 24 cm Issue [1. vyd.] Edition Undergraduate texts in mathematics , 0172-6056 ISBN 978-0-387-40293-2 Note Bibliografia s. 536-541. Reg. Keywords Booleove algebry algebra - algebra Boolean algebra Language English Country United States of America systematics 512 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xkni - BOOKS Copy count 1, currently available 0, at library only 1 
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Call number Location Sublocation Umiestnenie Info 316046 Univerzita Mateja Bela Department of mathematics In-Library Use Only Title The dimension of orthomodular posets constructed by pasting Boolean algebras Author info Alfonz Haviar, Pavel Hrnčiar Author Haviar Alfonz (50%) UMBFP10 - Katedra matematiky
Co-authors Hrnčiar Pavel 1951- (50%) UMBFP10 - Katedra matematiky
Source document Order : a journal on the theory of ordered sets and its applications. Vol. 10, no. 2 (1993), pp. 183-197. - Dordrecht : Springer Nature, 1993 Keywords Booleove algebry dimension Boolean algebra atomic amalgam Language English Country Netherlands systematics 51 Public work category ADE No. of Archival Copy 25447 Repercussion category AL-AGHA, Khaled J. Involutory dimension for involution posets : research report No. 96-01. Louisiana : Louisiana Tech University, April 1996, pp. 26.
AL-AGHA, KJ - GREECHIE, R. J. The involutory dimension of involution posets. In Order : a journal on the theory of ordered sets and its applications. ISSN 0167-8094, 2001, vol. 18, no. 4, pp. 323-337.
AL-AGHA, Khaled J. - GREECHIE, Richard J. Order dimension of orthomodular amalgamations over trees. In Order-a journal on the theory of ordered sets and its applications. ISSN 0167-8094, 2008, vol. 25, no. 1, pp. 55-68.
BERAN, L - SALVATI, S. Boolean algebras revisited. In Bollettino della unione matematica Italiana. ISSN 0041-7084, 1997, vol. 11B, no. 4, pp. 895-901.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article