O jednom pěkném algebraickém výsledku
Ojective ideals in modular lattices
The concept of an extending ideal in a modular lattice is introduced. A translation of module-theoretical concept of ojectivity (i.e. generalized relative injectivity) in the context of the lattice of ideals of a modular lattice is introduced. In a modular lattice satisfying a certain condition, a characterization is given for direct summands of an extending ideal to be mutually ojective. We define exchangeable decomposition and internal exchange property of an ideal in a modular lattice. It is...
On a weak Freudenthal spectral theorem
Let be an Archimedean Riesz space and its Boolean algebra of all band projections, and put and , . is said to have Weak Freudenthal Property () provided that for every the lattice is order dense in the principal band . This notion is compared with strong and weak forms of Freudenthal spectral theorem in Archimedean Riesz spaces, studied by Veksler and Lavrič, respectively. is equivalent to -denseness of in for every , and every Riesz space with sufficiently many projections...
On atoms in tolerance lattices of distributive lattices
On bounding congruences in some algebras having the lattice structure
On central relations of complete lattices
On compatible and order-preserving functions on lattices
On finitely generated multiplication modules
We shall prove that if is a finitely generated multiplication module and is a finitely generated ideal of , then there exists a distributive lattice such that with Zariski topology is homeomorphic to to Stone topology. Finally we shall give a characterization of finitely generated multiplication -modules such that is a finitely generated ideal of .
On generalized MS-Algebras
On ideals of a skew lattice
Ideals are one of the main topics of interest when it comes to the study of the order structure of an algebra. Due to their nice properties, ideals have an important role both in lattice theory and semigroup theory. Two natural concepts of ideal can be derived, respectively, from the two concepts of order that arise in the context of skew lattices. The correspondence between the ideals of a skew lattice, derived from the preorder, and the ideals of its respective lattice image is clear. Though,...
On midpoints in lattices
On -fold implicative filters of lattice implication algebras.
On -ideals of groups of divisibility
On perspectivities in incidence geometries of grade n
On regularity classes of binary relations
On skeletal and irreducible elements in tolerance lattices of finite distributive lattices
On some Jordan-Hölder-Dedekind type theorems in lattices.
On the complementation of relatively complemented distributive lattices
On the congruence lattice of stable algebras with definability of compact congruences
On the intersection of maximal filters in distributive lattices