Abstract
Let A be an archimedean f-algebra with unit element e, B be an archimedean semiprime f-algebra and T : A → B be a lattice (or Riesz) homomorphism. The main purpose of this paper is to show, in straightforward and elementary manner, that the range R(T) of T is an f-subalgebra of B if and only if Te is idempotent in B.
I would like to dedicate this paper to Professor Paul Conrad, whose papers influenced my research.
The author is grateful to both referees for pointing out some obscurities in the original version of this paper.
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© 2002 Springer Science+Business Media Dordrecht
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Boulabiar, K. (2002). The Range of Lattice Homomorphisms on f-Algebras. In: Martínez, J. (eds) Ordered Algebraic Structures. Developments in Mathematics, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3627-4_8
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DOI: https://doi.org/10.1007/978-1-4757-3627-4_8
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