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
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