Generalized - and -lattices of order ω+
Generalized prime -filters of distributive lattices
The concept of generalized prime -filters is introduced in distributive lattices. Generalized prime -filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime -filters is introduced in distributive lattices and properties of minimal prime -filters are then studied with respect to congruences. Some topological properties of the space of all prime -filters of a distributive lattice are also studied.
Generalized versions of MV-algebraic central limit theorems
MV-algebras can be treated as non-commutative generalizations of boolean algebras. The probability theory of MV-algebras was developed as a generalization of the boolean algebraic probability theory. For both theories the notions of state and observable were introduced by abstracting the properties of the Kolmogorov's probability measure and the classical random variable. Similarly, as in the case of the classical Kolmogorov's probability, the notion of independence is considered. In the framework...
Generated fuzzy implications and fuzzy preference structures
The notion of a construction of a fuzzy preference structures is introduced. The properties of a certain class of generated fuzzy implications are studied. The main topic in this paper is investigation of the construction of the monotone generator triplet , which is the producer of fuzzy preference structures. Some properties of mentioned monotone generator triplet are investigated.
Generating of a class of lattices and its application
Generating subsets of distributive lattices.
Geometric and higher order logic in terms of abstract Stone duality.
GMV-algebras and meet-semilattices with sectionally antitone permutations
Graph isomorphisms of modular multilattices
g-valoraciones de retículos distributivos.
Higher degrees of distributivity in -algebras
In this paper we deal with the of an -algebra , where and are nonzero cardinals. It is proved that if is singular and -distributive, then it is . We show that if is complete then it can be represented as a direct product of -algebras which are homogeneous with respect to higher degrees of distributivity.
Holland’s theorem for pseudo-effect algebras
We give two variations of the Holland representation theorem for -groups and of its generalization of Glass for directed interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo -algebra can be represented as a pseudo-effect algebra or as a pseudo -algebra of automorphisms of some antilattice or of some linearly ordered set.
Horizontal sums of basic algebras
The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.
Hu's Primal Algebra Theorem revisited
It is shown how Lawvere's one-to-one translation between Birkhoff's description of varieties and the categorical one (see [6]) turns Hu's theorem on varieties generated by a primal algebra (see [4], [5]) into a simple reformulation of the classical representation theorem of finite Boolean algebras as powerset algebras.
Ideals, congruences and annihilators on nearlattices
By a nearlattice is meant a join-semilattice having the property that every principal filter is a lattice with respect to the semilattice order. We introduce the concept of (relative) annihilator of a nearlattice and characterize some properties like distributivity, modularity or -distributivity of nearlattices by means of certain properties of annihilators.
Ideals, -rings and -algebras
Ideals of noncommutative -monoids
In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice ordered monoid and we show that congruence relations and certain ideals are in a one-to-one correspondence.
Idempotent distributive semirings II..
Imbedding locally convex lattices into compact lattices
Implication and equivalential reducts of basic algebras
A term operation implication is introduced in a given basic algebra and properties of the implication reduct of are treated. We characterize such implication basic algebras and get congruence properties of the variety of these algebras. A term operation equivalence is introduced later and properties of this operation are described. It is shown how this operation is related with the induced partial order of and, if this partial order is linear, the algebra can be reconstructed by means of...