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Residuated Lattices with Noetherian Spectrum

Author

Listed:
  • 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)

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.

Suggested Citation

  • Dana Piciu & Diana Savin, 2022. "Residuated Lattices with Noetherian Spectrum," Mathematics, MDPI, vol. 10(11), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1831-:d:824664
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