Multipliers in weak Heyting algebras

Document Type : Special Issue Dedicated to Prof. Esfandiar Eslami

Author

Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In this paper, we introduce the notion of multipliers in weak Heyting algebras and investigate some related properties of them. We obtain the relations between multipliers, closure operators, and homomorphisms in weak Heyting algebras. Relations among image sets and fixed point sets of multipliers in weak Heyting algebras are investigated. Also, we study algebraic structures of the set of all multipliers in weak Heyting algebras. Using multipliers, the left and right m-stabilizers in weak Heyting algebras are introduced, and some related properties are given. Also, we obtain conditions
such that the left and right m-stabilizers form two weak Heyting algebras.

Keywords

Main Subjects

References

[1] Ardeshir, M., & Ruitenburg, W. (1998). Basic propositional calculus I. Mathematical Logic Quarterly, 44(3), 317-343. http://dx.doi.org/10.1002/malq.19980440304
[2] Alizadeh, M., & Joharizadeh, N. (2015). Counting weak Heyting algebras on  nite distributive lattices. Logic Journal of the IGPL, 23(2), 247-258. http://dx.doi.org/10.1093/jigpal/jzu033
[3] Borzooei, R. A.,& Paad, A. (2012). Some new types of stabilizers in BL-algebras and their applications. Indian Journal of science and Technology, 5(1), 1910-1915. http://dx.doi.org/10.17485/ijst/2012/v5i1.29
[4] Busneag, D., & Piciu, D. (2005). BL-algebra of fractions and maximal BL-algebra of quotients. Soft Computing, 9, 544-555.http://dx.doi.org/10.1007/s00500-004-0372-9
[5] Celani, S., & Jansana, R. (2005). Bounded distributive lattices with strict implication. Mathematical Logic Quarterly, 51(3), 219-246. http://dx.doi.org/10.1002/malq.200410022
[6] Chaudhry, M. A., & Ali, F. (2012). Multipliers in d-algebras. World Applied Sciences Journal, 18(11), 1649-1653.
[7] Cirulis, J. (1986). Multipliers in implicative algebras. Bulletin of the Section of Logic, 15(4), 152-157.
[8] Cornish, W. H. (1974). The multiplier extension of a distributive lattice. Journal of Algebra, 32(2), 339-55. http://dx.doi.org/10.1016/0021-8693(74)90143-4
[9] Dan, C. (1997). F-multipliers and the localization of Heyting algebras. An. Univ. Craiova Ser. Mat. Inform, 24, 98-109.
[10] Ghorbani, S. (2013). Localization of hoop-algebras. J. Adv. Res. Pure Math, 5(3), 1-13. http://dx.doi.org/10.5373/jarpm.1378.032812
[11] Kim, K. H. (2011). Multipliers in BE-algebras. In International Mathematical Forum, 6(17), 815-820.
[12] Kim, K. H., & Lim, H. J. (2013). On Multipliers of BCC-algebras. Honam Mathematical Journal, 35(2), 201-210.  http://dx.doi.org/10.5831/HMJ.2013.35.2.201 
[13] Nourany, M., Ghorbani, S., & Saeid, A. B. (2023). On self-distributive weak Heyting algebras. Mathematical Logic Quarterly, 69(2), 192-206. http://dx.doi.org/10.1002/malq.202200073 
[14] San Martn, H. J. (2016). Principal congruences in weak Heyting algebras. Algebra universalis, 75, 405-418. http://dx.doi.org/10.1007/s00012-016-0381-4 
[15] Schmid, J. (1980). Multipliers on distributive lattices and rings of quotients. Houston Journal of Mathematics, 6(3), 401-425.
[16] Tayebi Khorami, R., & Borumand Saeid, A. (2014). Multiplier in BL-algebras. Iranian Journal of Science, 38(2), 95-103.
[17] Wang, J. T., He, P. F., & Borumand Saeid, A. (2018). Stabilizers in MTL-algebras. Journal of Intelligent & Fuzzy Systems, 35(1), 717-727. http://dx.doi.org/10.3233/JIFS-171105 
[18] Zhu, K., Wang, J., & Yang, Y. (2019). On two new classes of stabilizers in residuated lattices. Soft Computing, 23(23), 12209-12219.
Journal of Mahani Mathematical Research
Volume 13, Issue 4 - Serial Number 29
Special issue dedicated to Professor Esfandiar Eslami
December 2024
Pages 53-66

Files

History

  • Receive Date: 01 January 2024
  • Revise Date: 11 February 2024
  • Accept Date: 04 March 2024

Share

How to cite

Statistics