Abstract
In this paper, it is proven that a uniformly complete vector lattice A is normal if and only if the range of every extended orthomorphism in A is an order ideal of A. As an application, it is shown that a vector lattice A is hyper-Archimedean if and only if the range of every extended orthomorphism in A is a uniformly closed order ideal of A. Moreover, a complete description of Archimedean f-algebras with unit elements such that the range of every orthomorphism is an order ideal is given in terms of order, algebraic and topological properties.
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The author is very grateful to the referee for the careful reading of the paper and for his comments and detailed suggestions which helped to improve considerably the manuscript.
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Communicated by See Keong Lee.
This paper is dedicated to the memory of my father and of professor Abdelmajid Triki.
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Toumi, M.A. When the Range of Every Orthomorphism is an Order Ideal. Bull. Malays. Math. Sci. Soc. 43, 4289–4302 (2020). https://doi.org/10.1007/s40840-020-00922-x
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DOI: https://doi.org/10.1007/s40840-020-00922-x