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When a lattice homomorphism is a Riesz homomorphism

2006-01-01
Ercan, Z.
Wickstead, A. W.
Let E and F be uniformly complete vector lattices with disjoint complete systems (u(i))(i is an element of I) and (v(i))(i is an element of 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(lambda u(i)) = lambda v(i) for each lambda is an element of R and i is an element of I then T is linear. This generalizes the main results of [4] and [5]. (C) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.