Factorization by lattice homomorphisms

1984 ◽  
Vol 185 (4) ◽  
pp. 567-571 ◽  
Author(s):  
Wolfgang Arendt
Keyword(s):  
Lattice Homomorphisms

scholarly journals WHEN LATTICE HOMOMORPHISMS OF ARCHIMEDEAN VECTOR LATTICES ARE RIESZ HOMOMORPHISMS

2009 ◽  
Vol 87 (2) ◽  
pp. 263-273 ◽  
Author(s):  
MOHAMED ALI TOUMI
Keyword(s):  
London Math ◽  
Lattice Homomorphism ◽  
Vector Lattices ◽  
Lattice Homomorphisms ◽  
Orthogonal Systems

AbstractLet A, B be Archimedean vector lattices and let (ui)i∈I, (vi)i∈I be maximal orthogonal systems of A and B, respectively. In this paper, we prove that if T is a lattice homomorphism from A into B such that $T\left ( \lambda u_{i}\right ) =\lambda v_{i}$ for each λ∈ℝ+ and i∈I, then T is linear. This generalizes earlier results of Ercan and Wickstead (Math. Nachr279 (9–10) (2006), 1024–1027), Lochan and Strauss (J. London Math. Soc. (2) 25 (1982), 379–384), Mena and Roth (Proc. Amer. Math. Soc.71 (1978), 11–12) and Thanh (Ann. Univ. Sci. Budapest. Eotvos Sect. Math.34 (1992), 167–171).

MULTI-FUZZY EXTENSIONS OF FUNCTIONS

2011 ◽  
Vol 03 (03) ◽  
pp. 339-350 ◽  
Author(s):  
SABU SEBASTIAN ◽  
T. V. RAMAKRISHNAN
Keyword(s):  
Complete Lattice ◽  
Order Homomorphisms ◽  
Lattice Homomorphisms

In this paper, we study various properties of multi-fuzzy extensions of crisp functions using order homomorphisms, complete lattice homomorphisms, L-fuzzy lattices, and strong L-fuzzy lattices as bridge functions.

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