Ring-like structures corresponding to generalized orthomodular lattices
Ring-like structures derived from -lattices with antitone involutions
Using the concept of the -lattice introduced recently by V. Snášel we define -lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.
Ring-like structures with unique symmetric difference related to quantum logic
Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.
Semigroups and their lattice of congruences II.
Semigroups with Boolean Congruence Lattices.
Semi-ideals in semi-lattices
Semimodularity in lower continuous strongly dually atomic lattices
For lattices of finite length there are many characterizations of semimodularity (see, for instance, Grätzer [3] and Stern [6]–[8]). The present paper deals with some conditions characterizing semimodularity in lower continuous strongly dually atomic lattices. We give here a generalization of results of paper [7].
Semimodularity of the Congruence Lattice on Regular ...-Semigroups.
Semiprime ideals in orthomodular lattices
Separating points by prime filters in modular semilattices.
Separating points of measures on effect algebras
Separation conditions in relatively complemented lattices
Sheffer operation in ortholattices
We introduce the concept of Sheffer operation in ortholattices and, more generally, in lattices with antitone involution. By using this, all the fundamental operations of an ortholattice or a lattice with antitone involution are term functions built up from the Sheffer operation. We list axioms characterizing the Sheffer operation in these lattices.
Short Note: Counting Conjectures.
Some problems for measures on non-standard algebraic structures
Nell'ultimo ventennio tutta una serie di lavori è stata rivolta allo studio delle misure su strutture algebriche più generali delle algebre di Boole, come i poset e i reticoli ortomodulari, le effect algebras, le BCK-algebras. La teoria così ottenuta interessa l'analisi funzionale, il calcolo delle probabilità e la topologia, più recentemente la teoria delle decisioni. Si presentano alcuni risultati relativi a misure su strutture algebriche non-standard analizzando, in particolare, gli aspetti topologici...
Some properties of congurence relations on orthomodular lattices
In this paper congruences on orthomodular lattices are studied with particular regard to analogies in Boolean algebras. For this reason the lattice of p-ideals (corresponding to the congruence lattice) and the interplay between congruence classes is investigated. From the results adduced there, congruence regularity, uniformity and permutability for orthomodular lattices can be derived easily.
Some remarks on certain classes of semilattices.
Some remarks on modularity in prealgebraic and algebraic lattices
Some special subsets of intervals of a locally finite locally semi-modular, local lattice.
Spaces of observables