Dumitru Busneag, Dana Piciu, Liviu Holdon, Laura Dobre: Noetherian and Artinian algebras in the general case of residuated, 229-238

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.