Papers by Danica Jakubíková-studenovská
Algebra universalis, Mar 18, 2024
Equivalence relations or, more general, quasiorders (i.e., reflexive and transitive binary relati... more Equivalence relations or, more general, quasiorders (i.e., reflexive and transitive binary relations) have the property that an n-ary operation f preserves , i.e., f is a polymorphism of , if and only if each translation (i.e., unary polynomial function obtained from f by substituting constants) preserves , i.e., it is an endomorphism of. We introduce a wider class of relations-called generalized quasiorders-of arbitrary arities with the same property. With these generalized quasiorders we can characterize all algebras whose clone of term operations is determined by its translations by the above property, what generalizes affine complete algebras. The results are based on the characterization of so-called u-closed monoids (i.e., the unary parts of clones with the above property) as Galois closures of the Galois connection End-gQuord, i.e., as endomorphism monoids of generalized quasiorders. The minimal u-closed monoids are described explicitly.
Czechoslovak Mathematical Journal, Dec 1, 2000
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arXiv (Cornell University), Jul 4, 2023
Equivalence relations or, more general, quasiorders (i.e., reflexive and transitive binary relati... more Equivalence relations or, more general, quasiorders (i.e., reflexive and transitive binary relations) ϱ have the property that an n-ary operation f preserves ϱ, i.e., f is a polymorphism of ϱ, if and only if each translation (i.e., unary polynomial function obtained from f by substituting constants) preserves ϱ, i.e., it is an endomorphism of ϱ. We introduce a wider class of relations-called generalized quasiorders-of arbitrary arities with the same property. With these generalized quasiorders we can characterize all algebras whose clone of term operations is determined by its translations by the above property, what generalizes affine complete algebras. The results are based on the characterization of so-called u-closed monoids (i.e., the unary parts of clones with the above property) as Galois closures of the Galois connection End − gQuord, i.e., as endomorphism monoids of generalized quasiorders. The minimal u-closed monoids are described explicitly.
Czechoslovak Mathematical Journal, 1995
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Algebra and discrete mathematics, Apr 27, 2018
For a monounary algebra A = (A, f) we study the lattice Quord A of all quasiorders of A, i.e., of... more For a monounary algebra A = (A, f) we study the lattice Quord A of all quasiorders of A, i.e., of all reflexive and transitive relations compatible with f. Monounary algebras (A, f) whose lattices of quasiorders are complemented were characterized in 2011 as follows: (*) f (x) is a cyclic element for all x ∈ A, and all cycles have the same square-free number n of elements. Sufficiency of the condition (*) was proved by means of transfinite induction. Now we will describe a construction of a complement to a given quasiorder of (A, f) satisfying (*).
Czechoslovak Mathematical Journal, 1982
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Czechoslovak Mathematical Journal, Mar 1, 2005
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Mathematica Bohemica
The minimal nontrivial endomorphism monoids M = EndCon (A, F) of congruence lattices of algebras ... more The minimal nontrivial endomorphism monoids M = EndCon (A, F) of congruence lattices of algebras (A, F) defined on a finite set A are described. They correspond (via the Galois connection End-Con) to the maximal nontrivial congruence lattices Con (A, F) investigated and characterized by the authors in previous papers. Analogous results are provided for endomorphism monoids of quasiorder lattices Quord(A, F).
Czechoslovak Mathematical Journal, 1992
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Czechoslovak Mathematical Journal, 1993
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Czechoslovak Mathematical Journal
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Papers by Danica Jakubíková-studenovská