Congruences and Trajectories in Planar Semimodular Lattices
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2018, Vol 38, Issue 1
Abstract
A 1955 result of J. Jakub´ık states that for the prime intervals p and q of a finite lattice, con(p) ≥ con(q) iff p is congruence-projective to q (via intervals of arbitrary size). The problem is how to determine whether con(p) ≥ con(q) involving only prime intervals. Two recent papers approached this problem in different ways. G. Cz´edli’s used trajectories for slim rectangular lattices—a special subclass of slim, planar, semimodular lattices. I used the concept of prime-projectivity for arbitrary finite lattices. In this note I show how my approach can be used to reprove Cz´edli’s result and generalize it to arbitrary slim, planar, semimodular lattices.
Authors and Affiliations
G. Grätzer
Keywords
Related Articles
- EP ID EP394538
- DOI 10.7151/dmgaa.1280
- Views 63
- Downloads 0
ON THE AUTOTOPISM GROUP OF THE CORDERO-FIGUEROA SEMIFIELD OF ORDER 3^6
In [5] M. Biliotti, V. Jha and N. Johnson were able to completely determine the autotopism group of a generalized twisted field as a subgroup of ΓL(K) × ΓL(K), where K = GF(p^n) and ΓL(K) is the group of nonsingular semi...
Some finite directly indecomposable non-monogenic entropic quasigroups with quasi-identity
In this paper we show that there exists an infinite family of pairwise non-isomorphic entropic quasigroups with quasi-identity which are directly indecomposable and they are two-generated. Keywords: quasigroups, entropic...
AN EQUATIONAL AXIOMATIZATION OF POST ALMOST DISTRIBUTIVE LATTICES
In this paper, we prove that the class of P2-Almost Distributive Lattices and Post Almost Distributive Lattices are equationally definable.
NON-DETERMINISTIC LINEAR HYPERSUBSTITUTIONS
A non-deterministic hypersubstitution maps operation symbols to sets of terms of the corresponding arity. A non-deterministic hypersubstitution of type τ is said to be linear if it maps any operation symbol to a set of l...
Jordan numbers, Stirling numbers and sums of powers
In the paper a new combinatorical interpretation of the Jordan numbers is presented. Binomial type formulae connecting both kinds of numbers mentioned in the title are given. The decomposition of the product of polynomia...