Some examples of weakly associative lattices
Some finite congruence lattices, I
Some Maximal Closed Classes of Operations on Infinite Sets.
Some methods to obtain t-norms and t-conorms on bounded lattices
In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice based on a priori given t-norm acting on and t-conorm acting on for an arbitrary element . We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.
Some operations on lattice implication algebras.
Some primitive classes of lattices closed under the formation of projective images
Some properties of an ordering relation on certain classes of functors
Some properties of Eulerian lattices
In this paper, we prove that Eulerian lattices satisfying some weaker conditions for lattices or some weaker conditions for 0-distributive lattices become Boolean.
Some properties of lattice homomorphisms
Some properties of state filters in state residuated lattices
We consider properties of state filters of state residuated lattices and prove that for every state filter of a state residuated lattice :
Some properties of the weak subalgebra lattice of a partial algebra of a fixed type
We investigate, using results from [[p3]], when a given lattice is isomorphic to the weak subalgebra lattice of a partial algebra of a fixed type. First, we reduce this problem to the question when hyperedges of a hypergraph can be directed to a form of directed hypergraph of a fixed type. Secondly, we show that it is enough to consider some special hypergraphs. Finally, translating these results onto the lattice language, we obtain necessary conditions for our algebraic problem, and also, we completely...
Some simple extensions of Eulerian lattices.
Some types of implicative ideals
This paper studies basic properties for five special types of implicative ideals (modular, pentagonal, even, rectangular and medial). The results are used to prove characterizations of modularity and distributivity.
Span in incidence structures of independent sets defined on projective space
Special incidence structures of type
Special incidence structures of type . II.
Special measures and repleteness.
Standard completions for quasiordered sets.
States on unital partially-ordered groups
We study states on unital po-groups which are not necessarily commutative as normalized positive real-valued group homomorphisms. We show that in contrast to the commutative case, there are examples of unital po-groups having no state. We introduce the state interpolation property holding in any Abelian unital po-group, and we show that it holds in any normal-valued unital -group. We present a connection among states and ideals of po-groups, and we describe extremal states on the state space of...
Stone Lattices
The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the paper, the notion of a pseudocomplement in a lattice is formally introduced in Mizar, and based on this we define the notion of the skeleton and the set of dense elements in a pseudocomplemented lattice, giving the meet-decomposition of arbitrary element of a lattice as the infimum of two elements: one belonging to the skeleton, and the other which...