A note on tolerance lattices of finite chains
A note on tolerance lattices of products of lattices
A note on topology of -continuous posets
-continuous posets are common generalizations of continuous posets, completely distributive lattices, and unique factorization posets. Though the algebraic properties of -continuous posets had been studied by several authors, the topological properties are rather unknown. In this short note an intrinsic topology on a -continuous poset is defined and its properties are explored.
A note on uniserial loops
All ordinal numbers with the following property are found: there exists a loop such that its subloops form a chain of ordinal type .
A partically ordered space which is not a Priestely space.
A principal congruence identity characterizing the variety of distributive lattices with zero
A principal topology obtained from uninorms
We obtain a principal topology and some related results. We also give some hints of possible applications. Some mathematical systems are both lattice and topological space. We show that a topology defined on the any bounded lattice is definable in terms of uninorms. Also, we see that these topologies satisfy the condition of the principal topology. These topologies can not be metrizable except for the discrete metric case. We show an equivalence relation on the class of uninorms on a bounded lattice...
A property of the lattice of subsemilattices
A reduced free product of lattices
A regular a-semigroups inducing a certain lattice.
A relational semantics for the logic of bounded lattices
This paper aims to propose a complete relational semantics for the so-called logic of bounded lattices, and prove a completeness theorem with regard to a class of two-sorted frames that is dually equivalent (categorically) to the variety of bounded lattices.
A remark on the spectra of rings with Gabriel dimension
A representation theorem for CAC lattices.
A representation theorem for certain Boolean lattices.
Let R be an associative ring with 1 and R-tors the somplete Brouwerian lattice of all hereditary torsion theories on the category of left R-modules. A well known result asserts that R is a left semiartinian ring iff R-tors is a complete atomic Boolean lattice. In this note we prove that if L is a complete atomic Boolean lattice then there exists a left semiartinian ring R such that L is lattice-isomorphic to R-tors.
A result forO2-convergence to be topological in posets
In this paper, the α waybelow relation, which is determined by O2-convergence, is characterized by the order on a poset, and a sufficient and necessary condition for O2-convergence to be topological is obtained.
A selection property of the boolean -calculus and some of its applications
A simple basis of ideal terms of Brouwerian semilattices
A simple geometric proof of a theorem on
A solution of Dedekind's problem on the number of isotone Boolean functions.
A survey of hereditary properties of graphs
In this paper we survey results and open problems on the structure of additive and hereditary properties of graphs. The important role of vertex partition problems, in particular the existence of uniquely partitionable graphs and reducible properties of graphs in this structure is emphasized. Many related topics, including questions on the complexity of related problems, are investigated.