@article { author = {Georgescu, G.}, title = {Lattices of fractions and flat morphisms of bounded distributive lattices}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {1}, number = {4}, pages = {1-19}, year = {1999}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.1.4.1}, abstract = {The lattices of fractions were introduced by Brezuleanu and Diaconescu in 1969. They used this concept in order to construct a Grothendieck - style duality for the category D_{01} of bounded distributive lattices. Then the lattices of fraction}, keywords = {Lattices of fractions,flat lattices morphisms,flat topology}, url = {https://jahla.hatef.ac.ir/article_120333.html}, eprint = {https://jahla.hatef.ac.ir/article_120333_e2025f1a428cd3945fa031b7b444b486.pdf} } @article { author = {Keubeng Yemene, D.L. and Diekouam, L. and Akume, D. and Lele, C.}, title = {Some types of derivations in bounded commutative residuated lattices}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {1}, number = {4}, pages = {21-37}, year = {2020}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.1.4.2}, abstract = {In this paper, the notion of mutiplicative derivation, pseudo implicative derivation and implicative derivation on a bounded commutative residuated lattice are presented with some useful examples. We generalized these notions of derivation by introducing (f, g)-multiplicative derivation, (f, g)-pseudo implicative derivation and (f, g)-implicative derivation, and discussed some related properties; the conditions for (f, g)-multiplicative derivation, (f, g)-pseudo implicative derivation and (f, g)-implicative derivation to be monotone are provided. The set of fixed points is defined by using the notion of (f, g)-multiplicative derivation of bounded commutative residuated lattices. We also analyzed the link between different types of derivation.}, keywords = {Bounded commutative residuated lattice,Boolean algebra,derivation,set of fixed points,(F,g)-derivation}, url = {https://jahla.hatef.ac.ir/article_113802.html}, eprint = {https://jahla.hatef.ac.ir/article_113802_a448b79ea1c24dc66b91ad558a4982c8.pdf} } @article { author = {Xie, F. and Liu, H.}, title = {Ideals in pseudo-hoop algebras}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {1}, number = {4}, pages = {39-53}, year = {2020}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.1.4.3}, abstract = {Pseudo-hoop algebras are non-commutative generalizations of hoop-algebras, originally introduced by Bosbach. In this paper, we study ideals in pseudo-hoop algebras. We define congruences induced by ideals and construct the quotient structure. We show that there is a one-toone correspondence between the set of all normal ideals of a pseudo-hoop algebra A with condition (pDN) and the set of all congruences on A. Also, we prove that if A is a good pseudo-hoop algebra with pre-linear condition, then a normal ideal P of A is prime if and only if A/P is a pseudo-hoop chain. Furthermore, we analyse the relationship between ideals and filters of A. }, keywords = {Pseudo-hoop algebra,ideal,congruence,Filter}, url = {https://jahla.hatef.ac.ir/article_115370.html}, eprint = {https://jahla.hatef.ac.ir/article_115370_36b84974ee41a35317f4c2e0ae2725eb.pdf} } @article { author = {Farooq, M. and Khan, A. and Khan, R. and Izhar, M.}, title = {Characterization of ordered semihypergroups in terms of uni-soft bi-hyperideals}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {1}, number = {4}, pages = {55-70}, year = {1999}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.1.4.4}, abstract = {In this paper, we introduce the concept of unionsoft (briefly, uni-soft) bi-hyperideal of an ordered semihypergroup. The notions of prime (strongly prime, semiprime, irreducible, and strongly irreducible) uni-soft bi-hyperideals in ordered s}, keywords = {Uni-soft semi-hypergroup,prime (strongly prime),unisoft bi-hyperideal,semiprime uni-soft bi-hyperideal,irreducible (strongly irreducible) uni-soft bi-hyperideal,regular and intra-regular ordered semihypergroup}, url = {https://jahla.hatef.ac.ir/article_113605.html}, eprint = {https://jahla.hatef.ac.ir/article_113605_f5dd50b3808ee45c0da7ff98a4ee997d.pdf} } @article { author = {Mirvakili, S. and Naraghi, H.}, title = {Connections between reversible regular hypergroups, t-fuzzy subgroups and t-fuzzy graphs}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {1}, number = {4}, pages = {71-82}, year = {2020}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.1.4.5}, abstract = {In this paper, we obtain a reversible regular hypergroup from fuzzy sets by using a t-norm. Some properties of isomorphism of t-fuzzy graphs are considered and we show that a t-fuzzy subgroup can be associated with a t-fuzzy graph. Finally, using the group of automorphisms of fuzzy graph, we explain the relationship between the hypergroup and the t-fuzzy subgroup with the t-fuzzy graph.}, keywords = {Fuzzy graph,fuzzy subgroup,Hypergroup,t-norm}, url = {https://jahla.hatef.ac.ir/article_119855.html}, eprint = {https://jahla.hatef.ac.ir/article_119855_1fad194aea2c396618b5243e97d4bde5.pdf} } @article { author = {Paad, A.}, title = {On fuzzy implicative ideals in BL-algebras}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {1}, number = {4}, pages = {83-94}, year = {2020}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.1.4.6}, abstract = {In this paper, the concept of fuzzy implicative ideal in BL-algebras is introduced and several properties of it are stated. Using the concept of level subsets, some characterizations of fuzzy implicative ideals are proved. Also, it is proved that the concepts of fuzzy implicative ideal and fuzzy Boolean ideal in BL-algebras are coincide. Moreover, it is shown that a BL-algebra L is a Boolean algebra if and only if any fuzzy ideal of L is a fuzzy implicative ideal. Finally, it is proved that the homomorphic image and preimage of fuzzy implicative ideals are fuzzy implicative ideal.}, keywords = {BL-algebra,fuzzy implicative ideal,fuzzy Boolean ideal}, url = {https://jahla.hatef.ac.ir/article_120028.html}, eprint = {https://jahla.hatef.ac.ir/article_120028_6f75e24d4bcf665a2ac51521731c6f8c.pdf} } @article { author = {Rezazadeh, A. and Radfar, A.}, title = {Relation between hyper $K$-algebras with superlattices and hypersemilattices}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {1}, number = {4}, pages = {95-106}, year = {1999}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.1.4.7}, abstract = {In this paper, by considering the concepts of hypersemilattice and superlattice, we prove that any commutative and positive implicative hyper $K$-algebra, is a hypersemilattice. Moreover, we prove that any bounded commutative hyper $K$-algebra with some con}, keywords = {BCK-algebras,commutative hyper K-algebras,bounded hyper K-algebras,hypersemilattice,superlattice}, url = {https://jahla.hatef.ac.ir/article_119752.html}, eprint = {https://jahla.hatef.ac.ir/article_119752_95503bec23fbebfad7ff6c472a66e942.pdf} }