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Lattice Structure on Bounded Homomorphisms Between Topological Lattice Rings
Vladikavkaz Mathematical Journal 2019. Vol. 21. Issue 3.
Suppose \(X\) is a topological ring. It is known that there are three classes of bounded
group homomorphisms on \(X\) whose topological structures make them again topological rings. First, we show that if \(X\) is a Hausdorff topological ring, then so are these classes of bounded group homomorphisms on \(X\). Now, assume that \(X\) is a
locally solid lattice ring. In this paper, our aim is to consider lattice structure on these classes of bounded group
homomorphisms; more precisely, we show that, under some mild assumptions, they are locally solid lattice rings. In fact,
we consider bounded order bounded homomorphisms on \(X\). Then we show that under the assumed topology, they form locally
solid lattice rings. For this reason, we need a version of the remarkable Riesz-Kantorovich formulae for order bounded
operators in Riesz spaces in terms of order bounded homomorphisms on topological lattice groups.
Keywords: locally solid \(\ell\)-ring, bounded group homomorphism, lattice ordered ring.
Language: English Download the full text
For citation: Zabeti, O. Lattice Structure on Bounded Homomorphisms Between Topological Lattice Rings, Vladikavkaz Math. J., 2019, vol. 21, no. 3, pp. 14-23. DOI 10.23671/VNC.2019.3.36457
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