Laterally closed lattice homomorphisms
Copyright policy )Laterally closed lattice homomorphisms
A lattice homomorphism \(T: A\to B\) between two Archimedean vector lattices is called laterally closed if \(T(D)\) is a maximal orthogonal system in the band generated by \(T(A)\subset B\) for each maximal orthogonal system \(D\subset A\). The authors prove that any laterally closed \(T\) into a universally complete vector lattice \(B\) can be extended to a lattice homomorphism of the universal completion \(A^u\) into \(B\). This is an improvement of a result of \textit{M. Duhoux} and \textit{M. Meyer} [Ann. Soc. Sci. Bruxelles, Sér. I 98, 3--18 (1984; Zbl 0559.46003)].
Ordered rings, algebras, modules, Applied Mathematics, Laterally closed lattice homomorphism, laterally closed lattice homomorphism, \(d\)-algebra, Ordered abelian groups, Riesz groups, ordered linear spaces, d-algebra, f-algebra, \(f\)-algebra, Analysis, Ordered topological linear spaces, vector lattices
Ordered rings, algebras, modules, Applied Mathematics, Laterally closed lattice homomorphism, laterally closed lattice homomorphism, \(d\)-algebra, Ordered abelian groups, Riesz groups, ordered linear spaces, d-algebra, f-algebra, \(f\)-algebra, Analysis, Ordered topological linear spaces, vector lattices
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!