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Deciding active structural completeness
Authors:
- Michał Stronkowski
Abstract
We prove that if an n-element algebra generates the variety V which is actively structurally complete, then the cardinality of the carrier of each subdirectly irreduciblealgebra in V is at most n^[(n+1)*n^(2*n)]. As a consequence, with the use of known results, we show that there exist algorithms deciding whether a given finite algebraAgeneratesthe (actively) structurally complete variety V(A) in the cases when V(A) is congruence modular or V(A) is congruence meet-semidistributive or A is a semigroup.
- Record ID
- WUT79274566909a4422a77897003d23a97b
- Author
- Journal series
- Archive for Mathematical Logic, ISSN 0933-5846, e-ISSN 1432-0665
- Issue year
- 2020
- Vol
- 59
- Pages
- 149-165
- Publication size in sheets
- 0.80
- Keywords in Polish
- Strukturalna zupełność, Aktywna strukturalna zupełność, Rozstrzygalność, Skończenie generowane rozmaitości
- Keywords in English
- Structural completeness, Active structural completenes, Decidability, Finitely generated varieties
- ASJC Classification
- ;
- Abstract in Polish
- Pokazano, że jeśli A jest skończoną algebrą o n elementach, to każda podprosto nierozkładalna algebra w rozmaitości generowanej przez A ma no najwyżej n^[(n+1)*n^(2*n)] elementów. Dzięki temu, w paru istotnych przypadkach, udało się udowodnić istnienie algorytmów rozstrzygających czy dana skończona algebra generuje aktywnie strukturalną rozmaitość.
- DOI
- DOI:10.1007/s00153-019-00682-x Opening in a new tab
- URL
- https://link.springer.com/article/10.1007/s00153-019-00682-x Opening in a new tab
- Language
- eng (en) English
- License
- File
-
- File: 1
- Deciding active structural completeness, File WUT79274566909a4422a77897003d23a97b.pdf / 339 KB
- WUT79274566909a4422a77897003d23a97b.pdf
- publication date: 26-01-2022
- Deciding active structural completeness, File WUT79274566909a4422a77897003d23a97b.pdf / 339 KB
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- Score (nominal)
- 140
- Score source
- journalList
- Score
- = 140.0, 07-05-2022, ArticleFromJournal
- Publication indicators
- = 1; : 2018 = 0.973; : 2020 (2 years) = 0.287 - 2020 (5 years) =0.306
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- Uniform Resource Identifier
- https://repo.pw.edu.pl/info/article/WUT79274566909a4422a77897003d23a97b/
- URN
urn:pw-repo:WUT79274566909a4422a77897003d23a97b
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or PerishOpening in a new tab system.