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2021 | 50 | 1 | 81-96
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On GE-algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.
Rocznik
Tom
50
Numer
1
Strony
81-96
Opis fizyczny
Daty
wydano
2021-03-30
Twórcy
  • GITAM (Deemed to be University), Department of Mathematics, Hyderabad Campus, Telangana-502329, India
  • Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer, Kerman, Iran
  • Gyeongsang National University, Department of Mathematics Educations, Jinju 52828, Korea
Bibliografia
  • [1] J. C. Abbott, Semi-boolean algebra, Matematički Vesnik, vol. 4(19) (1967), pp. 177–198.
  • [2] R. A. Borzooei, S. Khosravi Shoar, Implication algebras are equivalent to the dual implicative BCK-algebras, Scientiae Mathematicae Japonicae, vol. 63(3) (2006), pp. 429–431.
  • [3] R. A. Borzooei, J. Shohani, On generalized Hilbert algebras, Italian Journal of Pure and Applied Mathematics, vol. 29 (2012), pp. 71–86.
  • [4] D. Buşneag, A note on deductive systems of a Hilbert algebra, Kobe Journal of Mathematics, vol. 2(1) (1985), pp. 29–35.
  • [5] D. Buşneag, Categories of algebraic logic, Editura Academiei Romane (2006).
  • [6] S. Celani, A note on homomorphisms of Hilbert algebras, International Journal of Mathematics and Mathematical Sciences, vol. 29(1) (2002), pp. 55–61, DOI: https://doi.org/10.1155/S0161171202011134
  • [7] W. Y. C. Chen, J. S. Oliveira, Implication algebras and the Metropolis-Rota axioms for cubic lattices, Journal of Algebra, vol. 171(2) (1995), pp. 383–396, DOI: https://doi.org/10.1006/jabr.1995.1017
  • [8] A. Diego, Sur les algèbres de Hilbert, Translated from the Spanish by Luisa Iturrioz. Collection de Logique Mathématique, Sér. A, Fasc. XXI, Gauthier-Villars, Paris; E. Nauwelaerts, Louvain (1966).
  • [9] A. Figallo, Jr., A. Ziliani, Remarks on Hertz algebras and implicative semilattices, Bulletin of the Section of Logic, vol. 34(1) (2005), pp. 37–42.
  • [10] A. V. Figallo, G. Z. Ramón, S. Saad, A note on the Hilbert algebras with infimum, Matemática Contemporânea, vol. 24 (2003), pp. 23–37, 8th Workshop on Logic, Language, Informations and Computation – WoLLIC'2001 (Brasília).
  • [11] S. M. Hong, Y. B. Jun, On deductive systems of Hilbert algebras, Korean Mathematical Society. Communications, vol. 11(3) (1996), pp. 595–600.
  • [11] Y. Imai, K. Iséki, On axiom systems of propositional calculi, XIV, Proceedings of the Japan Academy, vol. 42(1) (1966), pp. 19–22, DOI: https://doi.org/10.3792/pja/1195522169
  • [13] Y. B. Jun, Commutative Hilbert algebras, Soochow Journal of Mathematics, vol. 22(4) (1996), pp. 477–484.
  • [14] H. S. Kim, Y. H. Kim, On BE-algebras, Scientiae Mathematicae Japonicae, vol. 66(1) (2007), pp. 113–116.
  • [15] A. Monteiro, Lectures on Hilbert and Tarski Algebras, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca, Argentina (1960).
  • [16] A. A. Monteiro, Sur les algèbres de Heyting symétriques, Portugaliae Mathematica, vol. 39(1–4) (1980), pp. 1–237 (1985), special issue in honor of António Monteiro.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_18778_0138-0680_2020_20
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