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Natural extension of a congruence of a lattice to its lattice of convex sublattices

S. Parameshwara Bhatta, H. S. Ramananda (2011)

Archivum Mathematicum

Let L be a lattice. In this paper, corresponding to a given congruence relation Θ of L , a congruence relation Ψ Θ on C S ( L ) is defined and it is proved that 1. C S ( L / Θ ) is isomorphic to C S ( L ) / Ψ Θ ; 2. L / Θ and C S ( L ) / Ψ Θ are in the same equational class; 3. if Θ is representable in L , then so is Ψ Θ in C S ( L ) .

N-compact frames

Greg M. Schlitt (1991)

Commentationes Mathematicae Universitatis Carolinae

We investigate notions of ℕ -compactness for frames. We find that the analogues of equivalent conditions defining ℕ -compact spaces are no longer equivalent in the frame context. Indeed, the closed quotients of frame ‘ ℕ -cubes’ are exactly 0-dimensional Lindelöf frames, whereas those frames which satisfy a property based on the ultrafilter condition for spatial ℕ -compactness form a much larger class, and better embody what ‘ ℕ -compact frames’ should be. This latter property is expressible without reference...

Nearly disjoint sequences in convergence l -groups

Ján Jakubík (2000)

Mathematica Bohemica

For an abelian lattice ordered group G let G be the system of all compatible convergences on G ; this system is a meet semilattice but in general it fails to be a lattice. Let α n d be the convergence on G which is generated by the set of all nearly disjoint sequences in G , and let α be any element of G . In the present paper we prove that the join α n d ∨ α does exist in G .

Negation in bounded commutative D R ℓ -monoids

Jiří Rachůnek, Vladimír Slezák (2006)

Czechoslovak Mathematical Journal

The class of commutative dually residuated lattice ordered monoids ( D R ℓ -monoids) contains among others Abelian lattice ordered groups, algebras of Hájek’s Basic fuzzy logic and Brouwerian algebras. In the paper, a unary operation of negation in bounded D R ℓ -monoids is introduced, its properties are studied and the sets of regular and dense elements of D R ℓ -monoids are described.

New results for EP matrices in indefinite inner product spaces

Ivana M. Radojević (2014)

Czechoslovak Mathematical Journal

In this paper we study J -EP matrices, as a generalization of EP-matrices in indefinite inner product spaces, with respect to indefinite matrix product. We give some properties concerning EP and J -EP matrices and find connection between them. Also, we present some results for reverse order law for Moore-Penrose inverse in indefinite setting. Finally, we deal with the star partial ordering and improve some results given in the “EP matrices in indefinite inner product spaces” (2012), by relaxing some...

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