On ideals in Hilbert algebras
On ideals of a semilattice
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 ideals of implicative semigroups.
On ideals of lattice ordered monoids
In the paper the notion of an ideal of a lattice ordered monoid is introduced and relations between ideals of and congruence relations on are investigated. Further, it is shown that the set of all ideals of a soft lattice ordered monoid or a negatively ordered monoid partially ordered by inclusion is an algebraic Brouwerian lattice.
On idempotent modifications of -algebras
The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of a group is subdirectly irreducible. For an -algebra we denote by and the idempotent modification, the underlying set or the underlying lattice of , respectively. In the present paper we prove that if is semisimple and is a chain, then is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras.
On imaginable -fuzzy subalgebras and imaginable -fuzzy closed ideals in BCH-algebras.
On incidence algebras and directed graphs.
On indecomposable representations of quivers with zero-relations
On independence of the relations of epimorphy and embeddability on the variety of all lattices.
On infinite partition representations and their finite quotients
On infinitely distributive ordered sets
On integration in complete bornological locally convex spaces
A generalization of I. Dobrakov’s integral to complete bornological locally convex spaces is given.
On interval decomposition lattices
Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in an ordered set. They are defined abstractly as closed sets of a closure system on a set V, satisfying certain axioms. Decompositions are partitions of V whose blocks are intervals, and they form an algebraic semimodular lattice. Lattice-theoretical properties of decompositions are explored, and connections with particular types of intervals are established.
On interval homogeneous orthomodular lattices
An orthomodular lattice is said to be interval homogeneous (resp. centrally interval homogeneous) if it is -complete and satisfies the following property: Whenever is isomorphic to an interval, , in then is isomorphic to each interval with and (resp. the same condition as above only under the assumption that all elements , , , are central in ). Let us denote by Inthom (resp. Inthom) the class of all interval homogeneous orthomodular lattices (resp. centrally interval homogeneous...
On interval subalgebras of generalized MV-algebras
On intervals and isometries of -algebras
Let Int be the lattice of all intervals of an -algebra . In the present paper we investigate the relations between direct product decompositions of and (i) the lattice Int , or (ii) 2-periodic isometries on , respectively.
On intervals and the dual of a pseudo MV-algebra
On intra-regular ordered semigroups.
On intra-regular ve-semigroups.