Affine Complete Semilattices.
Affine completeness and lexicographic product decompositions of abelian lattice ordered groups
In this paper it is proved that an abelian lattice ordered group which can be expressed as a nontrivial lexicographic product is never affine complete.
Affine completeness and wreath product decompositions of lattice ordered group
Let and be a nonzero abelian linearly ordered group or a nonzero abelian lattice ordered group, respectively. In this paper we prove that the wreath product of and fails to be affine complete.
Affine completeness of complete lattice ordered groups
Affine completeness of de Morgan algebras
Affine completness of projectable lattice ordered groups
Affine permutations of type .
Aggregation for Quality Management
Aggregation operators on partially ordered sets and their categorical foundations
In spite of increasing studies and investigations in the field of aggregation operators, there are two fundamental problems remaining unsolved: aggregation of -fuzzy set-theoretic notions and their justification. In order to solve these problems, we will formulate aggregation operators and their special types on partially ordered sets with universal bounds, and introduce their categories. Furthermore, we will show that there exists a strong connection between the category of aggregation operators...
Algebra of observables and quantum logic
Algebraic and categorical properties of -ideal systems.
Algebraic and graph-theoretic properties of infinite -posets
A -labeled -poset is an (at most) countable set, labeled in the set , equipped with partial orders. The collection of all -labeled -posets is naturally equipped with binary product operations and -ary product operations. Moreover, the -ary product operations give rise to
Algebraic and graph-theoretic properties of infinite n-posets
A Σ-labeled n-poset is an (at most) countable set, labeled in the set Σ, equipped with n partial orders. The collection of all Σ-labeled n-posets is naturally equipped with n binary product operations and nω-ary product operations. Moreover, the ω-ary product operations give rise to nω-power operations. We show that those Σ-labeled n-posets that can be generated from the singletons by the binary and ω-ary product operations form the free algebra on Σ in a variety axiomatizable by an infinite collection...
Algebraic axiomatization of tense intuitionistic logic
We introduce two unary operators G and H on a relatively pseudocomplemented lattice which form an algebraic axiomatization of the tense quantifiers “it is always going to be the case that” and “it has always been the case that”. Their axiomatization is an extended version for the classical logic and it is in accordance with these operators on many-valued Łukasiewicz logic. Finally, we get a general construction of these tense operators on complete relatively pseudocomplemented lattice which is a...
Algebraic characterizations of special Boolean rings
Algebraic Classes of Abelian Torsion-Free and Lattice-Ordered Groups
Algebraic lattices are complete sublattices of the clone lattice over an infinite set
The clone lattice Cl(X) over an infinite set X is a complete algebraic lattice with compact elements. We show that every algebraic lattice with at most compact elements is a complete sublattice of Cl(X).
Algebraic properties of pre-logics
Algebraic representation of continua.
Algebraic shifting and sequentially Cohen-Macaulay simplicial complexes.