24 citations · 65 across the 15 of their papers we have counts for
8 papers · 1 filter
Conjecture on Maximal Sublattices of Finite Semidistributive Lattices and Beyond
K. Adaricheva, A. Mata, S. Silberger +1
We study maximal sublattices of finite semidistributive lattices via their complements. We focus on the conjecture that such complements are always intervals, which is known to be…
Barycentric algebras -- convexity and order
Anna Zamojska-Dzienio
This is the abstract of a series of lectures given during the XIIIth School on Geometry and Physics, Bialystok (Poland), in July 2024. In this minicourse, we first examine the alge…
Cocyclic braces and indecomposable cocyclic solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
We study indecomposable involutive set-theoretic solutions of the Yang-Baxter equation with cyclic permutation groups (cocyclic solutions). In particular, we show that there is no…
Semilattice ordered algebras with constants
Agata Pilitowska, Anna Zamojska-Dzienio
We continue our studies on semilattice ordered algebras. This time we accept constants in the type of algebras. We investigate identities satisfied by such algebras and describe th…
The retraction relation for biracks
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
In {\it Set-theoretical solutions to the quantum Yang-Baxter equation} (Duke Math. J. {\bf 100} (1999), 169--209), Etingof, Schedler and Soloviev introduced, for each non-degenerat…
Free medial quandles
Premysl Jedlicka, Agata Pilitowska, Anna Zamojska-Dzienio
This paper brings the construction of free medial quandles as well as free -symmetric medial quandles and free -reductive medial quandles.
Subdirectly irreducible medial quandles
Premysl Jedlicka, Agata Pilitowska, Anna Zamojska-Dzienio
We describe all subdirectly irreducible medial quandles. We show that they fall within one of four disjoint classes. In particular, in the finite case they are either connected (an…
Closure operators on algebras
Agata Pilitowska, Anna Zamojska-Dzienio
We study connections between closure operators on an algebra $(A,\Om)$ and congruences on the extended power algebra defined on the same algebra. We use these connections to give a…