Abstract:
In [6], Motamed and Moghaderi introduce the notions of noetherian and artinian BL algebras. In this paper, we generalize these
results, so we introduce the notions of noetherian and artinian
residuated lattices as lattices with the property that every increasing
(decreasing) chain of filters is stationary and we discuss them. We
translate some important results from theory of rings to the case of
residuated lattices: we prove the Cohen's theorem for residuated lattices
and we study the relation between noetherian (artinian) residuated lattices
in weak exact sequences.
Key Words: Noetherian (artinian) residuated
lattice, filter.
2010 Mathematics Subject Classification: Primary
08A72; Secondary 06F05, 06F10, 08A30.
