Residuated Lattices with Noetherian Spectrum

Dana Piciu and Diana Savin
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Dana Piciu: Department of Mathematics, Faculty of Science, University of Craiova, A. I. Cuza Street 13, 200585 Craiova, Romania
Diana Savin: Faculty of Mathematics and Computer Science, Transilvania University, Iuliu Maniu Street 50,500091 Braşov, Romania

Mathematics, 2022, vol. 10, issue 11, 1-13

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.

Keywords: Noetherian residuated lattice; ideal; prime ideal; Noetherian spectrum; ring of algebraic integers; Bezout rings; Dedekind rings (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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