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When a lattice homomorphism is a Riesz homomorphism
Author(s) -
Ercan Z.,
Wickstead A.W.
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410408
Subject(s) - homomorphism , mathematics , disjoint sets , lattice (music) , combinatorics , projection (relational algebra) , discrete mathematics , pure mathematics , physics , algorithm , acoustics
Let E and F be uniformly complete vector lattices with disjoint complete systems ( u i ) i ∈ I and ( v i ) i ∈ I of projection elements of E and F respectively. In this paper we prove that if T is a lattice homomorphism from E into F with T ( λu i ) = λv i for each λ ∈ ℝ and i ∈ I then T is linear. This generalizes the main results of [4] and [5]. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)