Hatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60003120220201Prof. Antonio Di Nola -- 3/4C?1314330910.52547/HATEF.JAHLA.3.1.1ENA.DvureˇcenskijMathematical Institute, Slovak Academy of Sciences, Stef´anikova 49, SK-814 73 Bratislava, Slovakia ˇ and
Palack´y University Olomouc, Faculty of Sciences, tˇr. 17. listopadu 12, CZ-771 46 Olomouc, Czech RepublicJournal Article20220116This article introduces Professor Di Nola, her life and research.https://jahla.hatef.ac.ir/article_143309_9b0d6ed5457970fbe78a807bd3c68dd7.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60003120220201A lattice-theoretical approach to extensions of filters in algebras of substructural logic51413662510.52547/HATEF.JAHLA.3.1.2END.SalounovaDepartment of Mathematical Methods in economy, Faculty of Economics, VSB-Technical University Ostrava, Sokolska 33, 701 21 Ostrava, Czech Republic0000-0002-2876-696XJ.RachunekDepartment of Algebra and Geometry,
Faculty of Sciences, Palacky University, 17. listopadu 12, 771 46 Olomouc, Czech Republic0000-0003-2986-960XJournal Article20210912Commutative bounded integral residuated lattices (residutaed lattices, in short) form a large class of algebras containing algebras which are algebraic counterparts of certain propositional fuzzy logics. The paper deals with the so-called extended filters of filters of residuated lattices. It is used the fact that the extended filters of filters associated with subsets coincide with those associated ones with corresponding filters. This makes it possible to investigate the set of all extended filters of residuated lattices within the Heyting algebras of their filters by means of the structural methods of the theory of such algebras.https://jahla.hatef.ac.ir/article_136625_f93b3b875087b711b5a0c5298ec478ed.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60003120220201New results on Congruence Boolean Lifting Property153413929710.52547/HATEF.JAHLA.3.1.3ENG.GeorgescuUniversity of Bucharest, Faculty of Mathematics and Computer Science, Bucharest, RomaniaJournal Article20211026The Lifting Idempotent Property (LIP) of ideals in commutative rings inspired the study of Boolean lifting properties in the context of other concrete algebraic structures (MV-algebras, commutative l-groups, BL-algebras, bounded distributive lattices, residuated lattices, etc.), as well as for some types of universal algebras (C. Muresan and the author defined and studied the Congruence Boolean Lifting Property (CBLP) for congruence modular algebras). A lifting ideal of a ring R is an ideal of R fulfilling LIP. In a recent paper, Tarizadeh and Sharma obtained new results on lifting ideals in commutative rings. The aim of this paper is to extend an important part of their results to congruences with CBLP in semidegenerate congruence modular algebras. The reticulation of such algebra will play an important role in our investigations (recall that the reticulation of a congruence modular algebra A is a bounded distributive lattice L(A) whose prime spectrum is homeomorphic with Agliano's prime spectrum of A). Almost all results regarding CBLP are obtained in the setting of semidegenerate congruence modular algebras having the property that the reticulations preserve the Boolean center. The paper contains several properties of congruences with CBLP. Among the results we mention a characterization theorem of congruences with CBLP. We achieve various conditions that ensure CBLP. Our results can be applied to a lot of types of concrete structures: commutative rings, l-groups, distributive lattices, MV-algebras, BL-algebras, residuated lattices, etc.<br /> https://jahla.hatef.ac.ir/article_139297_aac4bc40cc73c2b01a3d3a4de6936d8c.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60003120220201A short note on categorical equivalences of proper weak pseudo EMV-algebras354414034510.52547/HATEF.JAHLA.3.1.4ENA.DvureˇcenskijMathematical Institute, Slovak Academy of Sciences, Stef´anikova 49, SK-814 73 Bratislava, Slovakia ˇPalack´y University Olomouc, Faculty of Sciences, tˇr. 17. listopadu 12, CZ-771 46 Olomouc, Czech RepubliJournal Article20211119We study the class of weak pseudo EMV-algebras without top element that are a non-commutative generalization of MV-algebras, pseudo MV-algebras and generalized Boolean algebras. We present their categorical equivalences to a special category of pseudo MV-algebras with a fixed maximal and normal ideal as well as to a special category of unital l-groups with a fixed maximal and normal l-ideal.https://jahla.hatef.ac.ir/article_140345_7458027f0f98764dea650d29dd69f208.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60003120220201A longtime season of friendship and scientific collaboration456013500510.52547/HATEF.JAHLA.3.1.5ENR.GrigoliaDepartment o mathematics, Faculty of exact and Natural sciences, Tbilisi State University Tbilisi, GeorgiaJournal Article20210812The paper is devoted to a survey of Antonio Di Nola's, and Antonio Di Nola and Revaz Grigolia's scientific researches of longtime scientific collaboration.https://jahla.hatef.ac.ir/article_135005_6add893f1b95f7607961fb1b90edbcda.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60003120220201Unification in lax logic617513845810.52547/HATEF.JAHLA.3.1.6ENS.GhilardiUniversit\`a degli Studi di Milano, Department of Mathematics, via Cesare Saldini 50, 20133 MilanoG.LenziDIPMAT, University of Salerno, ItalyJournal Article20211009In this paper, we focus on the intuitionistic propositional logic extended with a local operator [22] (also called nucleus [21]); such logic is commonly named lax logic after [9]. We prove that unification is finitary in this logic and supply algorithms for computing a basis of unifiers and for recognizing admissibility of inference rules, following analogous known results for intuitionistic logic. <br /> https://jahla.hatef.ac.ir/article_138458_9502eef4201eff01e073b82589e6f118.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60003120220201Ultra deductive systems and (nilpotent) Boolean elements in hoops779313713310.52547/HATEF.JAHLA.3.1.7ENR.A.BorzooeiDepartment of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, IranY.B.JunDepartment of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea0000-0002-0181-8969M.AalyHatef Higher Education Institute, Zahedan, IranJournal Article20210919In this paper, first we define the concept of nilpotent element on a hoop H, study some properties of them and investigate the relation with ultra deductive systems. Then by using this notion, we introduce cyclic hoops and prove that every cyclic hoop has a unique generator and is a local MV-algebra. In the follows, we introduce the notion of Boolean elements on hoops and investigate some of their properties and relation among Boolean elements with ultra deductive systems and nilpotent elements. Finally, we introduce a functor between the category of hoops and category of Boolean elements of them.<br /> https://jahla.hatef.ac.ir/article_137133_dbcda696e0ad60c32c89c97ef305f9a9.pdf