Remarks on some connections between ideals and filters in residuated lattices

Dana Piciu; Christina Dan; Florentina Boboc

doi:10.2478/auom-2024-0024

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Remarks on some connections between ideals and filters in residuated lattices

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 32 (2024): Issue 2 (June 2024)

By: Dana Piciu, Christina Dan and Florentina Boboc

Open Access

|Jul 2024

Abstract

Ideals and filters are important notions with different meanings in the study of algebraic structures related to logical systems. In this paper we establish new connections between these concepts in residuated lattices.

References

Bu¸sneag, D., Piciu, D., A new approach for classification of filters in residuated lattices, Fuzzy Sets and Systems, 260 (2015), 121-130.
Search in Google Scholar Back to article
Bu¸sneag, D., Piciu, D., Dina, A., Ideals in residuated lattices, Carpathian J. Math., 37 (1) (2021), 53-63.
Search in Google Scholar Back to article
Cignoli, R., D’Ottaviano, I.M.L., Mundici, D., Algebraic Foundations of many-valued Reasoning, Trends in Logic-Studia Logica Library 7, Dordrecht: Kluwer Academic Publishers, 2000.
Search in Google Scholar Back to article
Idziak, P. M., Lattice operations in BCK-algebras, Math. Japonica, 29 (1984), 839-846.
Search in Google Scholar Back to article
Iorgulescu, A., Algebras of logic as BCK algebras, A.S.E., Bucharest, 2009.
Search in Google Scholar Back to article
Kondo, M., States on bounded commutative residuated lattices, Math. Slovaca, 64 (2014), 1093-1104.
Search in Google Scholar Back to article
Lele, C., Nganou, J.B., MV-algebras derived from ideals in BL-algebras, Fuzzy Sets and Systems 218 (2013), 103-113.
Search in Google Scholar Back to article
Leustean, L.,The prime and maximal spectra and the reticulation of BL-algebras, Centr. Eur. J. Math., 1 (3) (2003), 382-397.
Search in Google Scholar Back to article
Liu, Y., Qin, Y., Qin, X., Xu, Y., Ideals and fuzzy ideals in residuated lattices, Int. J. Math. Learn & Cyber, 8 (2017), 239-253.
Search in Google Scholar Back to article
Piciu, D., Algebras of fuzzy logic, Ed. Universitaria, Craiova, 2007.
Search in Google Scholar Back to article
Piciu, D., Prime, minimal prime and maximal ideals spaces in residuated lattices, Fuzzy Sets and Systems, 405 (2021), 47-64.
Search in Google Scholar Back to article
Turunen, E., Mathematics Behind Fuzzy Logic, Physica-Verlag, 1999.
Search in Google Scholar Back to article
Ward, M., Dilworth, R. P., Residuated lattices, Trans. Amer. Math. Soc. 45(3) (1939), 335-354.
Search in Google Scholar Back to article
Woumfo, F., Koguep Njionou, B., Alomo, E., Lele, C., Ideals and Bosbach states on residuated lattices, New Mathematics and Natural Computation, 16(3) (2020), 551-571.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/auom-2024-0024 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 145 - 155

Submitted on: May 3, 2023

Accepted on: Oct 21, 2023

Published on: Jul 10, 2024

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Residuated lattice,

filter,

ideal,

Related subjects:

© 2024 Dana Piciu, Christina Dan, Florentina Boboc, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 32 (2024): Issue 2 (June 2024)