On GE-algebras

Ravikumar Bandaru; Arsham Borumand Saeid; Young Bae Jun

Bulletin of the Section of Logic (2021)

  • Volume: 50, Issue: 1, page 81-96
  • ISSN: 0138-0680

Abstract

top
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.

How to cite

top

Ravikumar Bandaru, Arsham Borumand Saeid, and Young Bae Jun. "On GE-algebras." Bulletin of the Section of Logic 50.1 (2021): 81-96. <http://eudml.org/doc/296790>.

@article{RavikumarBandaru2021,
abstract = {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.},
author = {Ravikumar Bandaru, Arsham Borumand Saeid, Young Bae Jun},
journal = {Bulletin of the Section of Logic},
keywords = {(transitive) GE-algebra; filter; upper set; congruence kernel},
language = {eng},
number = {1},
pages = {81-96},
title = {On GE-algebras},
url = {http://eudml.org/doc/296790},
volume = {50},
year = {2021},
}

TY - JOUR
AU - Ravikumar Bandaru
AU - Arsham Borumand Saeid
AU - Young Bae Jun
TI - On GE-algebras
JO - Bulletin of the Section of Logic
PY - 2021
VL - 50
IS - 1
SP - 81
EP - 96
AB - 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.
LA - eng
KW - (transitive) GE-algebra; filter; upper set; congruence kernel
UR - http://eudml.org/doc/296790
ER -

References

top
  1. [1] J. C. Abbott, Semi-boolean algebra, Matematički Vesnik, vol. 4(19) (1967), pp. 177–198. 
  2. [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. [3] R. A. Borzooei, J. Shohani, On generalized Hilbert algebras, Italian Journal of Pure and Applied Mathematics, vol. 29 (2012), pp. 71–86. 
  4. [4] D. Buşneag, A note on deductive systems of a Hilbert algebra, Kobe Journal of Mathematics, vol. 2(1) (1985), pp. 29–35. 
  5. [5] D. Buşneag, Categories of algebraic logic, Editura Academiei Romane (2006). 
  6. [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. [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. [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. [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. [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. [11] S. M. Hong, Y. B. Jun, On deductive systems of Hilbert algebras, Korean Mathematical Society. Communications, vol. 11(3) (1996), pp. 595–600. 
  12. [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. [13] Y. B. Jun, Commutative Hilbert algebras, Soochow Journal of Mathematics, vol. 22(4) (1996), pp. 477–484. 
  14. [14] H. S. Kim, Y. H. Kim, On BE-algebras, Scientiae Mathematicae Japonicae, vol. 66(1) (2007), pp. 113–116. 
  15. [15] A. Monteiro, Lectures on Hilbert and Tarski Algebras, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca, Argentina (1960). 
  16. [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. 

NotesEmbed ?

top

You must be logged in to post comments.