This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice
Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the …

Symbol Explanation Page a∗(a∗) the unique lower (upper) cover of a 17 0I and 1I the zero
and unit of the interval I 12 Atom (U) set of atoms of the ideal U 106 Aut L automorphism …

We construct an algebraic distributive lattice D that is not isomorphic to the congruence
lattice of any lattice. This solves a long-standing open problem, traditionally attributed to RP …

Lattices with many congruences are planar Page 1 Algebra Univers. (2019) 80:16 c© 2019
The Author(s) 1420-8911/19/010001-11 published online March 2, 2019 https://doi.org/10.1007/s00012-019-0589-1 …

This work introduces tools, from the field of category theory, that make it possible to tackle
until now unsolvable representation problems (determination of the range of a given …

For a lattice L, let Princ (L) denote the ordered set of principal congruences of L. In a
pioneering paper, G. Grätzer proved that bounded ordered sets (in other words, posets with …

For a lattice L, let Princ (L) denote the ordered set of principal congruences of L. In a
pioneering paper, G. Grätzer characterized the ordered set Princ (L) of a finite lattice L; here …

For a lattice L with 0 and 1, let Princ (L) denote the set of principal congruences of L.
Ordered by set inclusion, it is a bounded ordered set. In 2013, G. Grätzer proved that every …

Abstract Let Lat^ sd _ 5 Lat 5 sd and Pos _ 01^\scriptscriptstyle+ Pos 01+ denote the
category of selfdual bounded lattices of length 5 with {0, 1\} 0, 1-preserving lattice …

We investigate the possible values of the numbers of congruences of finite lattices of an
arbitrary but fixed cardinality. Motivated by a result of Freese and continuing Czédli's recent …