Matches in SemOpenAlex for { <https://semopenalex.org/work/W2999266144> ?p ?o ?g. }
Showing items 1 to 87 of
87
with 100 items per page.
- W2999266144 abstract "Abstract Solution sets of systems of homogeneous linear equations over fields are characterized as being subspaces, i.e., sets that are closed under linear combinations. Our goal is to characterize solution sets of systems of equations over arbitrary finite algebras by a similar closure condition. We show that solution sets are always closed under the centralizer of the clone of term operations of the given algebra; moreover, the centralizer is the only clone that could characterize solution sets. If every centralizer-closed set is the set of all solutions of a system of equations over a finite algebra, then we say that the algebra has Property $${{,mathrm{(SDC)},}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mspace /><mml:mrow><mml:mo>(</mml:mo><mml:mi>SDC</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mspace /></mml:mrow></mml:math> . Our main result is the description of finite lattices and semilattices with Property $${{,mathrm{(SDC)},}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mspace /><mml:mrow><mml:mo>(</mml:mo><mml:mi>SDC</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mspace /></mml:mrow></mml:math> : we prove that a finite lattice has Property $${{,mathrm{(SDC)},}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mspace /><mml:mrow><mml:mo>(</mml:mo><mml:mi>SDC</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mspace /></mml:mrow></mml:math> if and only if it is a Boolean lattice, and a finite semilattice has Property $${{,mathrm{(SDC)},}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mspace /><mml:mrow><mml:mo>(</mml:mo><mml:mi>SDC</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mspace /></mml:mrow></mml:math> if and only if it is distributive." @default.
- W2999266144 created "2020-01-23" @default.
- W2999266144 creator A5012594167 @default.
- W2999266144 creator A5070313202 @default.
- W2999266144 date "2020-02-17" @default.
- W2999266144 modified "2023-10-07" @default.
- W2999266144 title "Solution sets of systems of equations over finite lattices and semilattices" @default.
- W2999266144 cites W1990617316 @default.
- W2999266144 cites W1992630510 @default.
- W2999266144 cites W2015623613 @default.
- W2999266144 cites W2031165112 @default.
- W2999266144 cites W2059030389 @default.
- W2999266144 cites W206333455 @default.
- W2999266144 cites W2149922426 @default.
- W2999266144 cites W2742830016 @default.
- W2999266144 cites W2888476830 @default.
- W2999266144 doi "https://doi.org/10.1007/s00012-020-0639-8" @default.
- W2999266144 hasPublicationYear "2020" @default.
- W2999266144 type Work @default.
- W2999266144 sameAs 2999266144 @default.
- W2999266144 citedByCount "1" @default.
- W2999266144 countsByYear W29992661442022 @default.
- W2999266144 crossrefType "journal-article" @default.
- W2999266144 hasAuthorship W2999266144A5012594167 @default.
- W2999266144 hasAuthorship W2999266144A5070313202 @default.
- W2999266144 hasBestOaLocation W29992661441 @default.
- W2999266144 hasConcept C111472728 @default.
- W2999266144 hasConcept C11821877 @default.
- W2999266144 hasConcept C118615104 @default.
- W2999266144 hasConcept C121332964 @default.
- W2999266144 hasConcept C132170107 @default.
- W2999266144 hasConcept C134306372 @default.
- W2999266144 hasConcept C136119220 @default.
- W2999266144 hasConcept C138885662 @default.
- W2999266144 hasConcept C146834321 @default.
- W2999266144 hasConcept C162324750 @default.
- W2999266144 hasConcept C162392398 @default.
- W2999266144 hasConcept C164953516 @default.
- W2999266144 hasConcept C189950617 @default.
- W2999266144 hasConcept C192606457 @default.
- W2999266144 hasConcept C202444582 @default.
- W2999266144 hasConcept C207405024 @default.
- W2999266144 hasConcept C24890656 @default.
- W2999266144 hasConcept C2781204021 @default.
- W2999266144 hasConcept C33923547 @default.
- W2999266144 hasConcept C34447519 @default.
- W2999266144 hasConcept C75174853 @default.
- W2999266144 hasConceptScore W2999266144C111472728 @default.
- W2999266144 hasConceptScore W2999266144C11821877 @default.
- W2999266144 hasConceptScore W2999266144C118615104 @default.
- W2999266144 hasConceptScore W2999266144C121332964 @default.
- W2999266144 hasConceptScore W2999266144C132170107 @default.
- W2999266144 hasConceptScore W2999266144C134306372 @default.
- W2999266144 hasConceptScore W2999266144C136119220 @default.
- W2999266144 hasConceptScore W2999266144C138885662 @default.
- W2999266144 hasConceptScore W2999266144C146834321 @default.
- W2999266144 hasConceptScore W2999266144C162324750 @default.
- W2999266144 hasConceptScore W2999266144C162392398 @default.
- W2999266144 hasConceptScore W2999266144C164953516 @default.
- W2999266144 hasConceptScore W2999266144C189950617 @default.
- W2999266144 hasConceptScore W2999266144C192606457 @default.
- W2999266144 hasConceptScore W2999266144C202444582 @default.
- W2999266144 hasConceptScore W2999266144C207405024 @default.
- W2999266144 hasConceptScore W2999266144C24890656 @default.
- W2999266144 hasConceptScore W2999266144C2781204021 @default.
- W2999266144 hasConceptScore W2999266144C33923547 @default.
- W2999266144 hasConceptScore W2999266144C34447519 @default.
- W2999266144 hasConceptScore W2999266144C75174853 @default.
- W2999266144 hasFunder F4320329149 @default.
- W2999266144 hasLocation W29992661441 @default.
- W2999266144 hasLocation W29992661442 @default.
- W2999266144 hasOpenAccess W2999266144 @default.
- W2999266144 hasPrimaryLocation W29992661441 @default.
- W2999266144 hasRelatedWork W13381172 @default.
- W2999266144 hasRelatedWork W19930168 @default.
- W2999266144 hasRelatedWork W22906802 @default.
- W2999266144 hasRelatedWork W32395600 @default.
- W2999266144 hasRelatedWork W33539964 @default.
- W2999266144 hasRelatedWork W35525179 @default.
- W2999266144 hasRelatedWork W54067882 @default.
- W2999266144 hasRelatedWork W55733950 @default.
- W2999266144 hasRelatedWork W61120698 @default.
- W2999266144 hasRelatedWork W9847657 @default.
- W2999266144 isParatext "false" @default.
- W2999266144 isRetracted "false" @default.
- W2999266144 magId "2999266144" @default.
- W2999266144 workType "article" @default.