Special polynomials in orthomodular lattices
States on basic algebras
States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which are the certain...
Stone lattices: a topological approach
Strong compact elements in multiplicative lattices
Structure des demi-groupes dont le treillis des sous-demi-groupes est semi-modulaire
Subalgebra modular, distributive and boolean varieties of semigroups
Subgraph isomorphism in planar graphs and related problems.
Sublattices with saturated chains
S-verklebte Summen von Verbänden.
Symmetric difference in orthomodular lattices
Symmetric difference on orthomodular lattices and -valued states
The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of -valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space.
Ternary spaces, media, and Chebyshev sets
The axioms for implication in orthologic
We set up axioms characterizing logical connective implication in a logic derived by an ortholattice. It is a natural generalization of an orthoimplication algebra given by J. C. Abbott for a logic derived by an orthomodular lattice.
The Brooks-Jewett theorem for -triangular functions on difference posets and orthoalgebras
The congruence variety of metabelian groups is not self-dual.
The Dimension Lattice of a JBW-Algebra.
The exocenter and type decomposition of a generalized pseudoeffect algebra
We extend the notion of the exocenter of a generalized effect algebra (GEA) to a generalized pseudoeffect algebra (GPEA) and show that elements of the exocenter are in one-to-one correspondence with direct decompositions of the GPEA; thus the exocenter is a generalization of the center of a pseudoeffect algebra (PEA). The exocenter forms a boolean algebra and the central elements of the GPEA correspond to elements of a sublattice of the exocenter which forms a generalized boolean algebra. We extend...
The lattice of pseudotopologies on S
The lattice of -subalgebras of a bounded distributive lattice
The lattice structure of quantum logics