Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585316120220101A new property of congruence lattices of slim, planar, semimodular lattices12810150810.52547/cgasa.2021.101508ENGábor Cz´edliBolyai Institute, University of Szeged, Szeged, Aradi H6720 Hungary0000-0001-9990-3573George Gr¨atzerUniversity of Manitoba, CanadaJournal Article20210924The systematic study of planar semimodular lattices started in<br />2007 with a series of papers by G. Grätzer and E. Knapp. These lattices have<br />connections with group theory and geometry. A planar semimodular lattice<br />L is slim if M3 it is not a sublattice of L. In his 2016 monograph, “The<br />Congruences of a Finite Lattice, A Proof-by-Picture Approach”, the second<br />author asked for a characterization of congruence lattices of slim, planar,<br />semimodular lattices. In addition to distributivity, both authors have previously<br />found specific properties of these congruence lattices. In this paper,<br />we present a new property, the Three-pendant Three-crown Property. The<br />proof is based on the first author’s papers: 2014 (multifork extensions), 2017<br />(C1-diagrams), and a recent paper (lamps), introducing the tools we need.https://cgasa.sbu.ac.ir/article_101508_ad42a5d1a69a3f6cc445ec82aaffc367.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585316120220101A new approach to tensor product of hypermodules295810153110.52547/cgasa.2021.101531ENSeyed Shahin MousaviDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran0000-0002-2904-7692Journal Article20211003As an essential tool in homological algebra, tensor products play a basic role in classifying and studying modules. Since hypermodules are generalization of modules, it is important to generalize the concept of the tensor products of modules to the hypermodules. In this paper, in order to achieve this goal, we present a more general form of the definition of hypermodule. Based on this new definition, some of the required concepts and properties have been studied. By obtaining a free object in the category of hypermodules, the notion of tensor product of hypermodules is provided and some of its properties are studied.https://cgasa.sbu.ac.ir/article_101531_c36b4b0a058e5bf4b4c6d9664402a9ce.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585316120220101Natural and restricted Priestley duality for ternary algebras and their cousins5910410159910.52547/cgasa.2021.101599ENBrian A.DaveyDepartment of Mathematics, La Trobe University, Victoria 3086,
Australia.Stacey P.MendanDepartment of Mathematics, La Trobe University, Victoria 3086, AustraliaJournal Article20211022Up to term equivalence, there are three ways to assign a nonempty<br />set C of constants to the three-element Kleene lattice, leading to<br />ternary algebras (C = {0, d, 1}), Kleene algebras (C = {0, 1}), and don’t<br />know algebras (C = {d}). Our focus is on ternary algebras. We derive<br />a strong, optimal natural duality and the restricted Priestley duality for<br />ternary algebras and give axiomatisations of the dual categories. We apply<br />these dualities in tandem to give straightforward and transparent proofs<br />of some known results for ternary algebras. We also discuss, and in some<br />cases prove, the corresponding dualities for Kleene lattices, Kleene algebras<br />and don’t know algebras.https://cgasa.sbu.ac.ir/article_101599_4ce0a2591e14df0d7224201fe6b49661.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585316120220101Quadratic structures associated to (multi)rings10514110143010.52547/cgasa.2021.101430ENKaique Matias De AndradeRobertoInstituto de Matem´atica e Estat´ıstica, Universidade de
S˜ao Paulo, Brazil.0000-0001-7136-8951Hugo Rafael De OliveiraRibeiroInstituto de Matem´atica e Estat´ıstica, Universidade de S˜ao
Paulo, BrazilHugo LuizMarianoInstituto de Matem´atica e Estat´ıstica, Universidade de
S˜ao Paulo, Brazil.0000-0002-9745-2411Journal Article20210831We consider certain pairs (A, T) where A is a (multi)ring and<br />T ⊆ A is a multiplicative set that generates, by a convenient quotient construction,<br />a (multi)structure that supports a quadratic form theory: with<br />some natural hypotheses we generalize constructions previously presented<br />in [3] and [6]. This also provides some steps towards an abstract formally<br />real quadratic form theory (non necessarily reduced) were the forms have<br />general coefficients (non only units).https://cgasa.sbu.ac.ir/article_101430_bb0f3ec01ae0ca89d6f8082aef1b5b76.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585316120220101Algebraic models of cubical weak ∞-categories with connections14318710153310.52547/cgasa.2021.101533ENCamell KachourLaboratoire de Math´ematiques d’Orsay, UMR 8628
Universit´e de Paris-Saclay and CNRS0009-0004-9550-1648Journal Article20211003In this article we adapt some aspects of Penon’s article [23] to cubical geometry. More precisely we define a monad on the category CSets of cubical sets (without degeneracies) whose algebras are models of cubical weak ∞-categories with connections.https://cgasa.sbu.ac.ir/article_101533_04e2a777ec95ba4c14b12d599ae71c2e.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585316120220101Algebraic models of cubical weak higher structures18922010154410.52547/cgasa.2021.101544ENCamell KachourLaboratoire de Mathématiques d’Orsay, UMR 8628
Université de Paris-Saclay and CNRS
Bâtiment 307, Faculté des Sciences d’Orsay0009-0004-9550-1648Journal Article20211005In this article we recast some of the results developped in articles [19, 22] but in the setup of cubical geometry. Thus we define a monad on ℂ𝕊ets whose algebras are models of cubical weak ∞-groupoids with connections. In addition, we define a monad on the category ℂ𝕊ets ×ℂ𝕊ets whose algebras are models of cubical weak ∞-functors, and a monad on the category ℂ𝕊ets ×ℂ𝕊ets ×ℂ𝕊ets ×ℂ𝕊ets whose algebras are models of cubical weak ∞-natural transformations.https://cgasa.sbu.ac.ir/article_101544_331b33b547e4eadc6d51fc63f0c9c84c.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585316120220101Fundamental groupoids for graphs22124810176610.52547/cgasa.2021.101766ENTien ChihMontana State University-Billings0000-0002-7278-5180Laura ScullFort Lewis CollegeJournal Article20211129In recent years several notions of discrete homotopy for graphs have been introduced, including a notion of ×-homotopy due to Dochtermann. In this paper, we define a ×-homotopy fundamental groupoid for graphs, and prove that it is a functorial ×-homotopy invariant for finite graphs. We also introduce tools to compute this fundamental groupoid, including a van Kampen theorem. We conclude with a comparison with previous definitions along these lines, including those built on polyhedral complexes of graph morphisms.https://cgasa.sbu.ac.ir/article_101766_3bc1a1701be553da8327d97fc712a071.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585316120220101Reflectional topology in MV-algebras24926710190710.52547/cgasa.2021.101907ENFereshteh ForouzeshFaculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran.Naser HosseiniDepartment of Pure Mathematics, Faculty of Math and Computers, Shahid Bahonar University of Kerman, Kerman, IranJournal Article20211223In this paper, we define soaker ideals in an MV-algebra, and study the relationships between soaker ideals and the other ideals in an involutive MV -algebras. Then we introduce a topology on the set of all the soaker ideals, which we call reflectional topology, and give a basis for it. By defining the notion of join-soaker ideals, we show that the reflectional topology is compact. We also give a characterization of connectedness of the reflectional topology. Finally, we investigate the properties of T0 and T1-space in this topology.https://cgasa.sbu.ac.ir/article_101907_2ded973e84d70c127553282fbd184a99.pdf