Article in volume
Authors:
Title:
$n$-fold fantastic and $n$-fold involutive ideals in bounded commutative residuated lattices
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 42(2) (2022) 363-381
Received: 2020-10-30 , Revised: 2021-05-10 , Accepted: 2022-05-31 , Available online: 2022-10-05 , https://doi.org/10.7151/dmgaa.1396
Abstract:
In this paper, we introduce the concepts of $n$-fold obstinate ideals, $n$-fold
normal ideals, $n$-fold fantastic ideals and $n$-fold involutive ideals in
residuated lattices, state and prove some of their properties. Several
characterizations of these notions are derived and the relations between those
notions are investigated. Also, we construct the correspondence between the
notions of $n$-fold ideal and $n$-fold filter in residuated lattices.
Keywords:
residuated lattice, ideal, $n$-fold ideal, $n$-fold filter
References:
- A. Ahadpanah and L. Torkzadeh, Normal filter in residuated lattices, Le Matematiche 70 (2015) 81–92.
https://doi.org/10.4418/2015.70.1.6 - R.A. Borzooei and A. Paad, Integral filters and integral BL-algebras, Italian J. Pure Appl. Math. 30 (2013) 303–316.
- R. Cretan and A. Jeflea, On the lattice of congruence filters of a residuated lattice, Annals of University of Craiova, Mathematics and Computer Science Series. 33 (2006) 174–188.
- F. Forouzesh, $n$-fold obstinate ideal in MV-algebras, New Math. Natural Comput. 12 (2016) 265–275.
https://doi.org/10.1142/S1793005716500186 - M. Haveshki, B. Saeid and E. Eslami, Some types of filters in BL-algebras, Soft Comput. 10 (2006) 657–664.
https://doi.org/10.1007/s00500-005-0534-4 - M. Haveshki and E. Eslami, n-fold filters in BL-algebra, Math. Log. Quart. 54 (2008) 176–186.
https://doi.org/10.1002/malq.200710029 - M. Haveshki and M. Mohamadhasani, Folding theory applied to Rl-monoid, Annals of the University of Craiova, Mathematics and Computer Science Series 37 (2010) 9–17.
- A. Kadji, C. Lele, J.B. Nganou and M. Tonga, Folding theory applied to residuated lattices, Int. J. Math. and Math. Sci. 4 (2014) 1–12.
https://doi.org/10.1155/2014/428940 - M. Kondo and W. Dudek, Filter theory of BL algebras, Soft Computing 12 (2009) 419–423.
https://doi.org/10.1007/s00500-007-0178-7 - C. Lele and S. Moutari, On some computational algorithms for n-fold ideals in BCK-algebras, J. Appl. Math. Comput. 23 (2007) 369–383.
https://doi.org/10.1007/BF02831984 - C. Lele and J.B. Nganou, MV-algebras derived from ideals in BL-algebras, Fuzzy Sets and Systems 218 (2013) 103–113.
https://doi.org/10.1016/j.fss.2012.09.014 - C. Lele and J.B. Nganou, Pseudo-addidion and fuzzy ideal in BL-algebras, Annals Math. Inform. 8 (2014) 193–207.
- Y. Liu, Y. Qin, X. Qin and Y. Xu, Ideals and fuzzy ideals on residuated lattices, Int. J. Machine Learning and Cybernetics, 8 (2014) 239–253.
https://doi.org/10.1007/s13042-014-0317-2 - S. Motamed and A.B. Saeid, n-fold obstinate filters in BL-algebras, Neural Comput. Appl. 20 (2011) 461–472.
https://doi.org/10.1007/s00521-011-0548-z - A. Paad and R.A. Borzooei, Generalization of integral filters in BL-algebras and n-fold integral BL-algebras, Africa Matematika 26 (2015) 1299–1311.
https://doi.org/10.1007/s13370-014-0275-6 - A. Paad, n-Fold integral ideals and n-fold Boolean ideals in BL-algebras, Africa Matematika 28 (2017) 971–984.
https://doi.org/10.1007/s13370-017-0497-5 - A. Paad, Folding theory of implicative and obstinate ideals in BL-algebras, Discuss. Math. Gen. Alg. and Appl. 38 (2018) 255–271.
https://doi.org/10.7151/dmgaa.1295 - A.B. Saeid and S. Motamed, Some results in BL-algebras, Math. Logic Quarterly 55 (2009) 649–658.
https://doi.org/10.1002/Malq.200910025 - Y.F. Tchoua, N.B.B. Koguep, A.E.R. Temgoua and C. Lele, $n$-fold boolean, implicative and integral ideals on bounded commutative residuated lattices, New Math. and Natural Comput. 15 (2019) 427–445.
https://doi.org/10.1142/S1793005719500248 - Y. Yang and X. Xin, On chracterizations of BL-algebras via implicative ideals, Italian J. Pure and Appl. Math. 37 (2017) 493–506.
- O. Zahiri and H. Farahani, n-Fold filters of MTL-algebras, Africa Matematika 25 (2014) 1165–1178.
https://doi.org/10.1007/s13370-013-0184-0
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