Pokaż uproszczony rekord

Radical and Jacobson Radical in L-Algebras

dc.contributor.authorBorzooei, Rajab Ali
dc.contributor.authorKhajeh Nasir, Hamideh
dc.contributor.authorYavari, Mehdi
dc.date.accessioned2026-10-21T11:13:43Z
dc.date.available2026-10-21T11:13:43Z
dc.date.issued2026-09-03
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/59539
dc.description.abstractIn this paper, inspired by the concepts of the radical of an ideal and the Jacobson radical in ring theory, we introduce these notions in the context of L-algebras. Our main goal is to explore the nature of the radical of an ideal and Jacobson radical in specific L-algebras. We successfully identify the elements of these radicals in special classes of L-algebras, including proper Glivenko algebras and finite Brouwerian semi-lattices using a closure operator. To achieve this goal, we introduce a new notion that is associated with any element a ∈ L as well as with an ideal of an L-algebra L.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;3en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectL-algebraen
dc.subjectCKL-algebraen
dc.subjectidealen
dc.subjectradical of an idealen
dc.subjectJacobson radicalen
dc.titleRadical and Jacobson Radical in L-Algebrasen
dc.typeOther
dc.page.number431-453
dc.contributor.authorAffiliationBorzooei, Rajab Ali - Soft Computing Center, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran; Department of Mathematics, Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkiyeen
dc.contributor.authorAffiliationKhajeh Nasir, Hamideh - Soft Computing Center, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iranen
dc.contributor.authorAffiliationYavari, Mehdi - Soft Computing Center, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iranen
dc.identifier.eissn2449-836X
dc.referencesP. B. Bhattacharya, S. K. Jain, S. R. Nagpaul, Basic Abstract Algebra, Cambridge University Press, Cambridge (1994).en
dc.referencesR. A. Borzooei, M. A. Kologani, G. R. Rezaei, Radical of Filters on Hoops,Iranian Journal of Fuzzy Systems, vol. 20(7) (2023), pp. 127–143, DOI: https://doi.org/10.22111/IJFS.2023.7661.en
dc.referencesS. Burris, H. P. Sankappanavar, A Course in Universal Algebra, Springer, New York and Heidelberg (1981).en
dc.referencesM. K. Chakraborty, J. Sen, MV-Algebras Embedded in a CL-Algebra,International Journal of Approximate Reasoning, vol. 18 (1998), pp. 217–229.en
dc.referencesL. C. Ciungu, Results in L-Algebras, Algebra Universalis, vol. 82(7) (2021), pp. 1–18, DOI: https://doi.org/10.1007/s00012-020-00695-1.en
dc.referencesV. G. Drinfeld, On Some Unsolved Problems in Quantum Group Theory, [in:] P. P. Kulish (ed.), Quantum Groups, vol. 1510 of Lecture Notes in Mathematics, Springer, Berlin (1992), pp. 1–8, DOI: https://doi.org/10.1007/BFb0101175.en
dc.referencesP. Etingof, Geometric Crystals and Set-Theoretical Solutions to the Quantum Yang–Baxter Equation, Communications in Algebra, vol. 31(4) (2003), pp. 1961–1973.en
dc.referencesT. Gateva-Ivanova, M. V. den Bergh, Semigroups of I-Type, Journal of Algebra, vol. 206(1) (1998), pp. 97–112, DOI: https://doi.org/10.1006/jabr.1997.7399.en
dc.referencesS. S. Goraghani, R. A. Borzooei, L-Modules, Bulletin of the Section of Logic, vol. 53(1) (2024), pp. 125–144, DOI: https://doi.org/10.18778/0138-0680.2023.27.en
dc.referencesS. S. Goraghani, R. A. Borzooei, Relationships between Various Ideals in L-Algebras, Soft Computing, vol. 29 (2025), pp. 2551–2562, DOI: https://doi.org/10.1007/s00500-025-10549-4.en
dc.referencesP. Köhler, Brouwerian Semilattices, Transactions of the American Mathematical Society, vol. 268(1) (1981), pp. 103–126, DOI: https://doi.org/10.2307/1998481.en
dc.referencesM. A. Kologani, Relations between L-Algebras and Other Logical Algebras, Journal of Algebraic Hyperstructures and Logical Algebras, vol. 4(1) (2023), pp. 27–46, DOI: https://doi.org/10.52547/HATEF.JAHLA.4.1.3.en
dc.referencesT. Moraschini, Orders, Lattices and Boolean Algebras, URL: https://moraschini.github.io/files/teaching/OLBA.pdf, lecture notes.en
dc.referencesH. K. Nasir, R. A. Borzooei, Prime and Primary Ideals on L-Algebras,Algebraic Structures and Their Applications, (2025), DOI: https://doi.org/10.22034/AS.2025.22295.1748, in press.en
dc.referencesH. K. Nasir, M. A. Kologani, R. A. Borzooei, Topology on Bounded CL -Algebras, Soft Computing, vol. 28 (2024), pp. 7617–7625, DOI: https://doi.org/10.1007/s00500-024-09728-6.en
dc.referencesW. Rump, A Decomposition Theorem for Square-Free Unitary Solutions of the Quantum Yang–Baxter Equation, Advances in Mathematics, vol. 193(1) (2005), pp. 40–55, DOI: https://doi.org/10.1016/j.aim.2004.03.019.en
dc.referencesW. Rump, L -Algebras, Self-Similarity, and ℓ -Groups, Journal of Algebra, vol. 320(6) (2008), pp. 2328–2348, DOI: https://doi.org/10.1016/j.jalgebra.2008.06.014.en
dc.referencesW. Rump, Semidirect Products in Algebraic Logic and Solutions of the Quantum Yang–Baxter Equation, Journal of Algebra and Its Applications, vol. 7(4) (2008), pp. 471–490, DOI: https://doi.org/10.1142/S0219498808002904.en
dc.referencesW. Rump, A General Glivenko Theorem, Algebra Universalis, vol. 61(3–4) (2009), pp. 455–473, DOI: https://doi.org/10.1007/s00012-009-0018-y.en
dc.referencesW. Rump, L -Algebras with Duality and the Structure Group of a Set-Theoretic Solution to the Yang–Baxter Equation, Journal of Pure and Applied Algebra, vol. 224(8) (2020), p. 106314, DOI: https://doi.org/10.1016/j.jpaa.2020.106314.en
dc.referencesW. Rump, L -Algebras and Three Main Non-Classical Logics, Annals of Pure and Applied Logic, vol. 173(11) (2022), p. 103121, DOI: https://doi.org/10.1016/j.apal.2022.103121.en
dc.referencesW. Rump, L. Vendramin, The Prime Spectrum of an L -Algebra, Proceedings of the American Mathematical Society, vol. 152 (2024), pp. 3197–3207, DOI: https://doi.org/10.1090/proc/16802.en
dc.referencesW. Rump, Y. Yang, Intervals in ℓ -Groups as L -Algebras, Algebra Universalis, vol. 67(2) (2012), pp. 121–130, DOI: https://doi.org/10.1007/s00012-012-0172-5.en
dc.referencesM. M. Takallo, Block Code on L -Algebras, Journal of Algebraic Hyperstructures and Logical Algebras, vol. 4(1) (2023), pp. 47–60, DOI: https://doi.org/10.52547/HATEF.JAHLA.4.1.4.en
dc.referencesX. Xin, X. Yang, Y. Ma, Pseudo L -Algebras, Iranian Journal of Fuzzy Systems, vol. 19(6) (2022), pp. 61–73, DOI: https://doi.org/10.22111/IJFS.2022.7210.en
dc.referencesB. Zeighami, M. M. Takallo, M. A. Kologani, S. S. Ahn, R. A. Borzooei, Classification of L -Algebras up to Order 4, Journal of Algebraic Hyperstructures and Logical Algebras, vol. 5(1) (2024), pp. 63–86, DOI: https://doi.org/10.61838/KMAN.JAHLA.5.1.7.en
dc.contributor.authorEmailBorzooei, Rajab Ali - borzooei@sbu.ac.ir
dc.contributor.authorEmailKhajeh Nasir, Hamideh - hamidehkhajehnasir@gmail.com
dc.contributor.authorEmailYavari, Mehdi - m_yavari@sbu.ac.ir
dc.identifier.doi10.18778/0138-0680.2026.14
dc.relation.volume55


Pliki tej pozycji

Thumbnail
Nazwa:
431-402_Borzooei_at_al..pdf
Rozmiar:
1.244MB
Format:
PDF
Oglądaj/Otwórz

Pozycja umieszczona jest w następujących kolekcjach

Pokaż uproszczony rekord

https://creativecommons.org/licenses/by-nc-nd/4.0
Poza zaznaczonymi wyjątkami, licencja tej pozycji opisana jest jako https://creativecommons.org/licenses/by-nc-nd/4.0