Residuated Lattices with Noetherian Spectrum

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 princi...

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 11; p. 1831
Main Authors Piciu, Dana, Savin, Diana
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 26.05.2022
Subjects
Algebra
Bezout rings
ideal
Lattices
Mathematics
Noetherian residuated lattice
Noetherian spectrum
prime ideal
ring of algebraic integers
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10111831