Abstract
In this paper, we characterize residuated lattices for which the topological space of prime ideals is a Noetherian space. The notion of i-Noetherian residuated lattice is introduced and related properties are investigated. We proved that a residuated lattice is i-Noetherian iff every ideal is principal. Moreover, we show that a residuated lattice has the spectrum of a Noetherian space iff it is i-Noetherian.
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