Generalizations of Boolean algebras. An attribute exploration
Generalizations of pseudo MV-algebras and generalized pseudo effect algebras
We deal with unbounded dually residuated lattices that generalize pseudo -algebras in such a way that every principal order-ideal is a pseudo -algebra. We describe the connections of these generalized pseudo -algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo -algebra by means of the positive cone of a suitable -group . We prove that the lattice of all (normal) ideals of and the lattice of all (normal) convex -subgroups of are isomorphic....
Generalized cardinal properties of lattices and lattice ordered groups
We denote by the class of all cardinals; put . Let be a class of algebraic systems. A generalized cardinal property on is defined to be a rule which assings to each an element of such that, whenever and , then . In this paper we are interested mainly in the cases when (i) is the class of all bounded lattices having more than one element, or (ii) is a class of lattice ordered groups.
Generalized Dedekind completion of a lattice ordered group
Generalized difference posets and orthoalgebras.
Generalized -semigroups
A semigroup is called a generalized -semigroup if there exists a group congruence on such that the identity class contains a greatest element with respect to the natural partial order of . Using the concept of an anticone, all partially ordered groups which are epimorphic images of a semigroup are determined. It is shown that a semigroup is a generalized -semigroup if and only if contains an anticone, which is a principal order ideal of . Also a characterization by means of the structure...
Generalized free products
A subalgebra B of the direct product of Boolean algebras is finitely closed if it contains along with any element f any other member of the product differing at most at finitely many places from f. Given such a B, let B* be the set of all members of B which are nonzero at each coordinate. The generalized free product corresponding to B is the subalgebra of the regular open algebra with the poset topology on B* generated by the natural basic open sets. Properties of this product are developed....
Generalized fuzzy ideals of BCI-algebras.
Generalized homogeneous, prelattice and MV-effect algebras
We study unbounded versions of effect algebras. We show a necessary and sufficient condition, when lattice operations of a such generalized effect algebra are inherited under its embeding as a proper ideal with a special property and closed under the effect sum into an effect algebra. Further we introduce conditions for a generalized homogeneous, prelattice or MV-effect effect algebras. We prove that every prelattice generalized effect algebra is a union of generalized MV-effect algebras and...
Generalized ideal elements in poe-semigroups.
Generalized intervals and topology
Generalized join-hemimorphisms on Boolean algebras.
Generalized lattice identities in lattice ordered groups
Generalized ordering and partitions
Generalized -lattices of order ω+
Generalized - and -lattices of order ω+
Generalized periodic and generalized Boolean rings.
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.