University of HatefJournal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Cover-Vol 1- Issue 4- November 2020120332ENJournal Article20201212http://jahla.hatef.ac.ir/article_120332_7753bc18574198075a11addf0472f03d.pdfUniversity of HatefJournal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Lattices of fractions and flat morphisms of bounded distributive lattices119120333ENG.GeorgescuUniversity of Bucharest, Faculty of Mathematics and Computer Science, Bucharest, RomaniaJournal Article20201212The 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 fractions are studied in connection with other themes in lattice theory: lattices schemas, localization of bounded distributive lattices, sheaf representations of normal lattices,etc. This paper continues this research vein. We relate the lattices of fractions to flat lattice morphisms, patch and flat topologies on the spectra of bounded distributive lattices, conormal and Stone lattices, etc. We define the flat morphisms of D_{01} in terms of the residuation operation existing in the frames of lattice ideals. We study how the lattices of fractions preserve the flatness property of morphisms. Two characterization theorems of flat and patch topologies are proved. The lattices of fractions are used for obtaining new characterizations of conormal and Stone lattices. http://jahla.hatef.ac.ir/article_120333_4646232f8fd35a2f08f247dbcae004d6.pdfUniversity of HatefJournal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Some types of derivations in bounded commutative residuated lattices2137113802ENDarline LaureKeubeng YemeneDepartment of Mathematics and Computer Science,
University of Dschang,
CameroonLucDiekouamDepartement of Mathematics
Higher Teachers' Training College
University of maroua
CamerounDanielAkumeComputer Science Department, HTTTC Kumba
University of Buea,
CameroonCelestinLeleDepartment 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.http://jahla.hatef.ac.ir/article_113802_ab068d851d0aeeddaf9afc86969a1aa5.pdfUniversity of HatefJournal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Ideals in pseudo-hoop algebras3953115370ENFeiXieSchool of Mathematics and Statistics, Shandong Normal University,
Jinan, P.R.ChinaHongxingLiuSchool 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. http://jahla.hatef.ac.ir/article_115370_4d30d8abc99a4051c80f5abf2497ac60.pdfUniversity of HatefJournal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Characterization of ordered semihypergroups in terms of uni-soft bi-hyperideals5570113605ENMuhammadFarooqAbdul Wali Khan University MardanAsgharKhanAbdul Wali Khan University MardanRaeesKhanDepartment of Mathematics, FATA University, Kohat, KP, PakistanMuhammadIzharDepartment of Mathematics Abdul Wali Khan University MardanJournal Article20200902In 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 semihypergroups are introduced and related properties are investigated. Numerous examples of these notions are given. The relationship between prime and strongly prime, irreducible and strongly irreducible uni-soft bi-hyperideals are considered and characterizations of these concepts are established. Regular and intra-regular ordered semihypergroups are characterized in terms of these notions.http://jahla.hatef.ac.ir/article_113605_bb17f7c8cb37b307fc5947dbe6638910.pdfUniversity of HatefJournal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Connected between reversible regular hypergroups, t-fuzzy subgroups and t-fuzzy graphs7182119855ENS.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.http://jahla.hatef.ac.ir/article_119855_0bb1b29fb781e9507e61879172471a72.pdfUniversity of HatefJournal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101On fuzzy implicative ideals in BL-algebras8394120028ENA.PaadDepartment of Mathematics, University of Bojnord, Bojnord, IranJournal 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.http://jahla.hatef.ac.ir/article_120028_831d36b77bed3c1f74e1eaca7050a549.pdfUniversity of HatefJournal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Relation between hyper $K$-algebras with superlattices and hypersemilattices95106119752ENAfaghRezazadehDepartment of Mathematics, Maku Branch, Islamic Azad University, Maku, IranAkefeRadfarDepartment of Mathematics, Payame Noor University, p. o. box. 19395-3697, Tehran, IranJournal Article20201127In 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 conditions, is a superlattice.http://jahla.hatef.ac.ir/article_119752_0366280d55b5ff622a92286f9200ac8e.pdfUniversity of HatefJournal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Persian translation of abstracts107115120335ENJournal Article20201212http://jahla.hatef.ac.ir/article_120335_b1776a3443dbcffde1fb99e4021de7b2.pdf