منابع مشابه
Weak Relative Pseudo-Complements of Closure Operators
We define the notion of weak relative pseudo-complement on meet semi-lattices, and we show that it is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main result is that if a complete lattice L is meet-continuous, then every closure operator on L admits weak relative pseudo-complements with respect to continuous closure operators on L.
متن کاملWeak Relative Pseudo - Complements of Closure OperatorsRoberto
We deene the notion of weak relative pseudo-complement, and we show that, for an arbitrary lattice, the property of weak relative pseudo-complementation is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main interest for this notion is in relation with the theory of closure operators. We prove that if a complete lattice L is completely inf-di...
متن کاملON THE STRUCTURE OF FINITE PSEUDO- COMPLEMENTS OF QUADRILATERALS AND THEIR EMBEDDABILITY
A pseudo-complement of a quadrilateral D of order n, n, > 3, is a non-trivial (n+l)- regular linear space with n - 3n + 3 points and n + n - 3 lines. We prove that if n > 18 and D has at least one line of size n - 1, or if n > 25 , then the set of lines of D consists of three lines of size n -1, 6(n - 2) lines of size n - 2, and n - 5n + 6 lines of size n - 3. Furthermore, if n > 21 and D...
متن کاملAnnulets of Stone lattices generated by pseudo-complements
The notion of pseudo-annulets is introduced in Stone lattices and characterized in terms of prime filters. Two operator α and β are introduced and obtained that their composition β ◦α is a closure operator on the class of all filters of a Stone lattice. A congruence θ is introduced on a Stone lattice L and proved that the quotient lattice L/θ is a Boolean algebra.
متن کاملPseudo Schur complements, pseudo principal pivot transforms and their inheritance properties
Extensions of the Schur complement and the principal pivot transform, where the usual inverses are replaced by the Moore-Penrose inverse, are revisited. These are called the pseudo Schur complement and the pseudo principal pivot transform, respectively. First, a generalization of the characterization of a block matrix to be an M -matrix is extended to the nonnegativity of the Moore-Penrose inve...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0272687-x