DIRECTLY INDECOMPOSABLE RESIDUATED LATTICES

Document Type: Research Paper

Author

Polytechnical University of Bucharest, Splaiul Independentei 313, Bucharest, Romania

Abstract

The aim of this paper is to extend results established by H. Ono
and T. Kowalski regarding directly indecomposable commutative residuated
lattices to the non-commutative case. The main theorem states that a residuated
lattice A is directly indecomposable if and only if its Boolean center B(A)
is {0, 1}. We also prove that any linearly ordered residuated lattice and any
local residuated lattice are directly indecomposable. We apply these results to
prove some properties of the Boolean center of a residuated lattice and also
define the algebras on subintervals of residuated lattices.

Keywords


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