When a lattice homomorphism is a Riesz homomorphism | Zendy

Ercan Z. | Zendy; Wickstead A.W. | Zendy

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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)

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