University of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001419991130Lattices of fractions and flat morphisms of bounded distributive lattices11912033310.52547/HATEF.JAHLA.1.4.1ENG. GeorgescuUniversity of Bucharest, Faculty of Mathematics and Computer Science, Bucharest, RomaniaJournal Article19991130The 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 fractionhttps://jahla.hatef.ac.ir/article_120333_e2025f1a428cd3945fa031b7b444b486.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Some types of derivations in bounded commutative residuated lattices213711380210.52547/HATEF.JAHLA.1.4.2END.L. Keubeng YemeneDepartment of Mathematics and Computer Science,
University of Dschang,
CameroonL. DiekouamDepartement of Mathematics
Higher Teachers' Training College
University of maroua
CamerounD. AkumeComputer Science Department, HTTTC Kumba
University of Buea,
CameroonC. LeleDepartment of Mathematics and Computer Science,
University of Dschang,
CameroonJournal Article20200907In 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.https://jahla.hatef.ac.ir/article_113802_a448b79ea1c24dc66b91ad558a4982c8.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Ideals in pseudo-hoop algebras395311537010.52547/HATEF.JAHLA.1.4.3ENF. XieSchool of Mathematics and Statistics, Shandong Normal University,
Jinan, P.R.ChinaH. LiuSchool of Mathematics and Statistics, Shandong Normal University,
Jinan, P.R.ChinaJournal Article20201003Pseudo-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. https://jahla.hatef.ac.ir/article_115370_36b84974ee41a35317f4c2e0ae2725eb.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001419991130Characterization of ordered semihypergroups in terms of uni-soft bi-hyperideals557011360510.52547/HATEF.JAHLA.1.4.4ENM. FarooqAbdul Wali Khan University MardanA. KhanAbdul Wali Khan University MardanR. KhanDepartment of Mathematics, FATA University, Kohat, KP, PakistanM. IzharDepartment of Mathematics Abdul Wali Khan University MardanJournal Article19991130In 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 shttps://jahla.hatef.ac.ir/article_113605_f5dd50b3808ee45c0da7ff98a4ee997d.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Connections between reversible regular hypergroups, t-fuzzy subgroups and t-fuzzy graphs718211985510.52547/HATEF.JAHLA.1.4.5ENS. MirvakiliDepartment of mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iranhttps://orcid.org/00H. NaraghiDepartment Mathematics, Payame Noor University, Tehran, Iran.Journal Article20201201In 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.https://jahla.hatef.ac.ir/article_119855_1fad194aea2c396618b5243e97d4bde5.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101On fuzzy implicative ideals in BL-algebras839412002810.52547/HATEF.JAHLA.1.4.6ENA. PaadDepartment of Mathematics, University of Bojnord, Bojnord, Iran0000-0003-0929-9830Journal Article20201206In 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.https://jahla.hatef.ac.ir/article_120028_6f75e24d4bcf665a2ac51521731c6f8c.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001419991130Relation between hyper $K$-algebras with superlattices and hypersemilattices9510611975210.52547/HATEF.JAHLA.1.4.7ENA. RezazadehDepartment of Mathematics, Maku Branch, Islamic Azad University, Maku, Iran0000-0002-2439-0141A. RadfarDepartment of Mathematics, Payame Noor University, p. o. box. 19395-3697, Tehran, IranJournal Article19991130In 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 conhttps://jahla.hatef.ac.ir/article_119752_95503bec23fbebfad7ff6c472a66e942.pdf