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Abstract. In the present paper there are introduced and investigated the notions of fractal and semifractal lattice ordered groups or Riesz groups, respectively. The definitions are related to those which have been applied in the lattice theory. Besides, there is shown the existence of a proper class of Boolean algebras which are semifractal lattices but fail to be fractal lattices.
AMS Subject Classification
(1991): 06F15, 06D35
Keyword(s):
lattice ordered group ($\ell $-group,
for short),
fractal,
semifractal,
homogeneous Boolean algebra,
Carathéodory functions
Received April 19, 2010, and in revised form November 23, 2010. (Registered under 30/2010.)
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