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Keywords = Noetherian residuated lattice

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13 pages, 298 KiB  
Article
Residuated Lattices with Noetherian Spectrum
by Dana Piciu and Diana Savin
Mathematics 2022, 10(11), 1831; https://doi.org/10.3390/math10111831 - 26 May 2022
Cited by 1 | Viewed by 1686
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 [...] Read more.
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. Full article
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