Decomposition of regular subsemigroup lattices.
Decompositions in lattices and some representations of algebras [Book]
Decompositions of semigroups with zero.
Dedekind completions of lattices by ends
Dedekind cuts in C(X)
The aim of this paper is to show that every Hausdorff continuous interval-valued function on a completely regular topological space X corresponds to a Dedekind cut in C(X) and conversely.
Degrees of compatible -subsets and compatible mappings
Based on a completely distributive lattice , degrees of compatible -subsets and compatible mappings are introduced in an -approximation space and their characterizations are given by four kinds of cut sets of -subsets and -equivalences, respectively. Besides, some characterizations of compatible mappings and compatible degrees of mappings are given by compatible -subsets and compatible degrees of -subsets. Finally, the notion of complete -sublattices is introduced and it is shown that the...
Demonic semantics: using monotypes and residuals.
Denotational aspects of untyped normalization by evaluation
We show that the standard normalization-by-evaluation construction for the simply-typed -calculus has a natural counterpart for the untyped -calculus, with the central type-indexed logical relation replaced by a “recursively defined” invariant relation, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal forms,...
Denotational aspects of untyped normalization by evaluation
We show that the standard normalization-by-evaluation construction for the simply-typed λβη-calculus has a natural counterpart for the untyped λβ-calculus, with the central type-indexed logical relation replaced by a “recursively defined” invariant relation, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal...
Dense extensions of a partially ordered set.
Derivations and Translations on Trellises
G. Szász, J. Szendrei, K. Iseki and J. Nieminen have made an extensive study of derivations and translations on lattices. In this paper, the concepts of meet-translations and derivations have been studied in trellises (also called weakly associative lattices or WA-lattices) and several results in lattices are extended to trellises. The main theorem of this paper, namely, that every derivatrion of a trellis is a meet-translation, is proved without using associativity and it generalizes a well-known...
Determinant of Some Matrices of Field Elements
Here, we present determinants of some square matrices of field elements. First, the determinat of 2 * 2 matrix is shown. Secondly, the determinants of zero matrix and unit matrix are shown, which are equal to 0 in the field and 1 in the field respectively. Thirdly, the determinant of diagonal matrix is shown, which is a product of all diagonal elements of the matrix. At the end, we prove that the determinant of a matrix is the same as the determinant of its transpose.
Die Abgeschlossenheit der lexikographischen Summe in der Klasse modularer Verbände
Die arithmetische Operation der Summe
Die Operationen in der Klasse komplementärer Verbände
Dimension Raising Maps in Topological Algebra.
Dimension raising maps in topological spaces.
Dimensionally stable semilattices.
Direct decomposability of tolerances on lattices, semilattices and quasilattices
Direct product decompositions of infinitely distributive lattices
Let be an infinite cardinal. Let be the class of all lattices which are conditionally -complete and infinitely distributive. We denote by the class of all lattices such that is infinitely distributive, -complete and has the least element. In this paper we deal with direct factors of lattices belonging to . As an application, we prove a result of Cantor-Bernstein type for lattices belonging to the class .