We study the lattice structure of fuzzy A-ideals in an mv-module M (fai (M), symbolically) and show that it is a complete Heyting lattice and so the set of its pseudocomplements forms a Boolean algebra. In the sequel, the properties of fuzzy congruences in an mv-module are investigated and using them some structural theorems are stated and proved. Finally, it is proved that fai (M) can be embedded into the lattice of fuzzy congruences.
BakhshiM., L-fuzzy A-Ideals of MV-modules, International Journal of Mathematics and Computation28 (2017), 107–119.
2.
BakhshiM. and BorzooeiR.A., Lattice structure on fuzzy congruence relations of a hypergroupoid, Information Sciences177 (2007), 3305–3313.
3.
BanivahebH. and BorumandA., Saeid, MV-modules of fractions, Journal of Algebra and Its Applications19 (2020), ID: 2050131.
4.
BedeB. and Di NolaA., Elementary calculus in Riesz MV-algebras, International Journal of Approximate Reasoning36 (2004), 129–149.
5.
BelluceL.P., Di NolaA. and LenziG., Algebraic geometry for MV-algebras, Journal of Symbolic Logic79 (2014), 1061–1091.
6.
BlythT.S., Lattices and ordered algebraic structures, Springer-Verlag, 2005.
7.
BorzooeiR.A., DvurecenskijA. and ZahiriO., State BCK algebras and state-morphism BCK-algebras, Fuzzy Sets and Systems244 (2014), 86–105.
8.
ChangC.C., Algebraic analysis of many valued logics, Transactions of the American Mathematical Society88 (1958), 467–490.
9.
CignoliR.L., D’OttavianoI.M. and MundiciD., Algebraic Foundations of Many-valued Reasoning, Springer Science & Business Media, 2013.
10.
Di Nola ndA. and DvurečenskijA., Product MV-algebras, Multiple-Valued Logic6 (2001), 193–215.
11.
Di NolaA., FlondorP. and LeusteanI., MV-modules, Journal of Algebra276 (2003), 21–40.
12.
Di NolaA., GrigoliaR. and LipartelianiR., On the free - free algebras, Journal of Algebraic Hyperstructures and Logical Algebras1 (2020), 1–7.
13.
Di NolaA. and LettieriA., Perfect MV-algebras are categorically equivalent to abelian ‘-groups, Studia Logica53 (1994), 417–432.
14.
DvurecenskijA., , A short note on categorical equivalences of proper weak EMV-algebras, Journal of Algebraic Hyperstructures and Logical Algebras3 (2022), 35–44.
15.
ForouzeshF., Fuzzy A-ideals in MV-modules, Annals of Fuzzy Mathematics and Informatics10 (2015), 477–486.
HooC.S., Fuzzy implicative and Boolean ideals of MValgebras, Fuzzy Sets and Systems66 (1994), 315–327.
18.
HooC.S., Fuzzy ideals of BCI and MV-algebras, Fuzzy Sets and Systems62 (1994), 111–114.
19.
PaadA. and BakhshiM., Hyper equality ideals: Basic properties, Journal of Algebraic Hyperstructures and Logical Algebras1(2) (2020), 45–56.
20.
RachůnekJ., DRL-semigroups and MV-algebras, Czechoslovak Mathematical Journal48 (1998), 365–372.
21.
SankappanavarH.P. and BurrisS., A Course in Universal Algebra, Graduate Text in Mathematics78, 1981.
22.
Saidi GoraghaniS. and BorzooeiR.A., On Injective MVModules, Bulletin of the Section of Logic47 (2018), 283–298.
23.
Saidi GoraghaniS. and BorzooeiR.A., Most results on Aideals in MV-modules, Journal of Algebraic Systems5 (2017), 1–13.
24.
Saidi GoraghaniS., BorzooeiR.A., AhnS.S. and JunY.B., New kind of MV-modules, International Journal of Computational Intelligence Systems13 (2020), 794–801.
25.
Saidi GoraghaniS. and BorzooeiR.A., Module structure on effect algebras, Bulletin of the Section of Logic49 (2020), 269–290.
26.
Saidi GoraghaniS. and BorzooeiR.A., Results on prime ideals in PMV-algebras and MV-modules, Italian Journal of Pure and Applied Mathematics37 (2017), 183–196.
27.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
28.
ZhangX., BorzooeiR.A. and JunY.B., Q-filters of quantum B-algebras and basic implication algebras,ID:, Symmetry10 (2018), 573.
