Anna Zamojska-Dzienio

ON LATTICES EMBEDDABLE INTO LATTICES OF ORDER-CONVEX SETS: CASE OF TREES

We find a syntactic characterization of the class of lattices embeddable into convexity lattices of posets which are trees. The characterization implies that this class forms a finitely based variety.

On some congruences of power algebras

In a natural way we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (A, Ω) its power algebra of subsets. In this paper we investigate extended power algebras (power algebras of non-empty subsets with one additional semilattice operation) of modes (entropic and idempotent algebras). We describe some congruence relations on these algebras such that their quotients are idempotent. Such congruences determine some class of non-trivial subvarieties of the variety of all semilattice ordered modes (modals).

Representation of modals

Abstract The main aim of this paper is to describe the free objects in arbitrary varieties of modals (semilattice ordered idempotent and entropic algebras) and give some new representations of modals.

Lattices of Order-Convex Sets of Forests

We give a characterization of the class

The Lattice of Subvarieties of Semilattice Ordered Algebras

\mathbf{Co}(\mathcal{F})

Lattices of subclasses. II

[

Lattices of subclasses

\mathrm{\mathbf{Co}}(\mathcal{F}_n)

Free medial quandles

, n < ω, respectively] of lattices isomorphic to convexity lattices of posets which are forests [forests of length at most n, respectively], as well as of the class

Closure operators on algebras

\mathbf{Co}(\mathcal{L})

Subdirectly irreducible medial quandles

of lattices isomorphic to convexity lattices of linearly ordered posets. This characterization yields that the class of finite members from