Constructive complete distributivity IV

1994 ◽  
Vol 2 (2) ◽  
pp. 119-144 ◽  
Author(s):  
Robert Rosebrugh ◽  
R. J. Wood
Keyword(s):  
Complete Distributivity

Linear types and approximation

2000 ◽  
Vol 10 (6) ◽  
pp. 719-745 ◽  
Author(s):  
MICHAEL HUTH ◽  
ACHIM JUNG ◽  
KLAUS KEIMEL
Keyword(s):  
Full Subcategory ◽  
Linear Logic ◽  
Domain Theory ◽  
Classical Domain ◽  
Complete Distributivity ◽  
Linear Types ◽  
Continuous Lattices

We study continuous lattices with maps that preserve all suprema rather than only directed ones. We introduce the (full) subcategory of FS-lattices, which turns out to be *-autonomous, and in fact maximal with this property. FS-lattices are studied in the presence of distributivity and algebraicity. The theory is extremely rich with numerous connections to classical Domain Theory, complete distributivity, Topology and models of Linear Logic.

scholarly journals Complete distributivity and ordered group lattices

1985 ◽  
Vol 95 (1) ◽  
pp. 79-79 ◽  
Author(s):  
Cecelia Laurie
Keyword(s):  
Ordered Group ◽  
Complete Distributivity

Compactness and Complete Distributivity for Commutative Subspace Lattices

1990 ◽  
Vol s2-42 (1) ◽  
pp. 147-159 ◽  
Author(s):  
Kenneth R. Davidson ◽  
David R. Pitts
Keyword(s):  
Complete Distributivity ◽  
Subspace Lattices

scholarly journals Quasi-atoms and complete distributivity

1988 ◽  
Vol 103 (2) ◽  
pp. 365-365 ◽  
Author(s):  
Zi Ke Deng
Keyword(s):  
Complete Distributivity

IRREDUCIBLE ELEMENTS IN ALGEBRAIC LATTICES

2010 ◽  
Vol 20 (08) ◽  
pp. 969-975 ◽  
Author(s):  
U. M. SWAMY ◽  
B. VENKATESWARLU
Keyword(s):  
Universal Algebra ◽  
Complete Lattice ◽  
Sufficient Conditions ◽  
Algebraic Lattice ◽  
Complete Distributivity ◽  
Lattice Of Subalgebras ◽  
Irreducible Elements ◽  
Algebraic Lattices ◽  
Strongly Irreducible ◽  
Necessary And Sufficient

α-Irreducible and α-Strongly Irreducible Ideals of a ring have been characterized in [2] and [4]. A complete lattice which is generated by compact elements is called an algebraic lattice for the simple reason that every such lattice is isomorphic to the lattice of subalgebras of a suitable universal algebra and vice-versa. In this paper, we characterize the irreducible elements and strongly irreducible elements in an algebraic lattice, which extends the results in [4] to arbitrary algebraic lattices. Also we obtain certain necessary and sufficient conditions, in terms of irreducible elements, for an algebraic lattice to satisfy the complete distributivity.

Further Properties of the Lattice of Torsion Classes of Abelian Cyclically Ordered Groups

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Judita Lihová ◽  
Ján Jakubík
Keyword(s):  
Torsion Class ◽  
Complete Distributivity ◽  
Fundamental Properties ◽  
Ordered Groups ◽  
Dual Atom

AbstractThe notion of torsion class of abelian cyclically ordered groups has been introduced and fundamental properties of the collection T of all such classes, ordered by the class-theoretical inclusion, have been proved by the second author in 2011. The present paper can be considered as a continuation of the above mentioned one. We describe all atoms of T , show that T does not have any dual atom and prove complete distributivity of T .

Distributivity and an axiom of choice

1954 ◽  
Vol 19 (4) ◽  
pp. 275-277 ◽  
Author(s):  
George E. Collins
Keyword(s):  
Axiom Of Choice ◽  
Complete Distributivity ◽  
Similar Proof ◽  
Image Position

In this paper a theorem will be established which states that a particular axiom of choice is equivalent to complete distributivity of union and intersection. The theorem will be formulated and proved in the system of logic of [4]. In addition to definitions of [4], the following will be used.In terms of these definitions, the theorem can be formulated as follows.The dual of this statement, obtained by interchanging I and U, is also a theorem and has a similar proof.

Constructive complete distributivity II

1991 ◽  
Vol 110 (2) ◽  
pp. 245-249 ◽  
Author(s):  
Robert Rosebrugh ◽  
R. J. Wood
Keyword(s):  
Complete Lattice ◽  
Left Adjoint ◽  
Complete Distributivity ◽  
Completely Distributive

AbstractA complete lattice, L, is constructively completely distributive, (CCD) (L), if the sup map defined on down-closed subobjects has a left adjoint. It was known that in Boolean toposes (CCD) (L) is equivalent to (CCD) (Lop). We show here that the latter property for all L (sufficiently, for Ω.) characterizes Boolean toposes.

scholarly journals Tight Galois connections and complete distributivity

1960 ◽  
Vol 97 (3) ◽  
pp. 418-418 ◽  
Author(s):  
George N. Raney
Keyword(s):  
Complete Distributivity ◽  
Galois Connections

scholarly journals When does a semiring become a residuated lattice?

2016 ◽  
Vol 09 (04) ◽  
pp. 1650088
Author(s):  
Ivan Chajda ◽  
Helmut Länger
Keyword(s):  
Residuated Lattice ◽  
Residuated Lattices ◽  
The Other ◽  
Natural Question ◽  
Double Negation ◽  
Complete Distributivity ◽  
Completely Distributive ◽  
Double Negation Law ◽  
The Given ◽  
Converse Assertion

It is an easy observation that every residuated lattice is in fact a semiring because multiplication distributes over join and the other axioms of a semiring are satisfied trivially. This semiring is commutative, idempotent and simple. The natural question arises if the converse assertion is also true. We show that the conversion is possible provided the given semiring is, moreover, completely distributive. We characterize semirings associated to complete residuated lattices satisfying the double negation law where the assumption of complete distributivity can be omitted. A similar result is obtained for idempotent residuated lattices.

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