Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585324120260101D-inverse constellations12810629510.48308/cgasa.2025.236863.1519ENVictoriaGouldDepartment of Mathematics, University of York, York, YO10 5GH, United KingdomTimothyStokesMathematics, School of Computing and Mathematical Sciences, University of Waikato, Hamilton, New Zealand0000-0003-2908-8563Journal Article20240910Constellations are partial algebras in the sense that they possess a partial product, and a unary operation modelling domain. They were first used to give an ESN-style theorem for left restriction semigroups in terms of so-called inductive constellations. Here, we consider constellations in which elements have a suitable notion of inverse, giving the notion of a D-inverse constellation. We show that there is a categorical isomorphism between the category of ordered groupoids and the category of D-inverse constellations. This may be viewed as a generalisation of the ESN theorem, which relates the category of inductive groupoids to the category of inverse semigroups.https://cgasa.sbu.ac.ir/article_106295_d17dc1fe0d8c0a8bd81d05587a73d9d0.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585324120260101$\mathcal{H}$-Fibrations: Fibrations in Homotopy Category294110494010.48308/cgasa.2024.234981.1474ENAliPakdamanDepartment of Mathematics, Faculty of Science, Golestan university,
P.O.Box 155, Gorgan, Iran0000-0002-6174-1043SabaDehrooyeDepartment of Mathematics, Faculty of Science, Golestan university,
P.O.Box 155, Gorgan, IranMehdiTajikDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran.BehroozMashayekhyDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran.Journal Article20240304In this paper we generalize fibrations by $\mathcal{H}$-fibrations, the maps which homotopically lift homotopies. We replace the equalities in the definition of covering homotopy property with the homotopy relation so that we can first get an expression of the concept of covering homotopy property in the homotopy category. After introducing $\mathcal{H}$-fibrations, we will have a homotopy expression of some concepts related to fibration, such as path lifting, lifting function and unique path lifting property, to generalize some results in fibration. In particular, we show that an $\mathcal{H}$-fibration has homotopical path lifting property and also prove that a map is an $\mathcal{H}$-fibration if and only if it has a homotopical lifting function.https://cgasa.sbu.ac.ir/article_104940_2dfc3a15689edfc90305c507af86e7e9.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585324120260101On the homomorphisms of $\cap$-structure spaces436210505210.48308/cgasa.2024.235060.1476ENElhamAbdollahpourDepartment of Mathematics, Faculty of Mathematical Science and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranAli RezaeiAliabadDepartment of Mathematics, Faculty of Mathematical Science and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran0000-0003-1293-3652JamalHashemiDepartment of Mathematics, Faculty of Mathematical Science and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20240317 In \cite{cap}, the concept of $\cap$-structure space is defined and it is studied from an algebraic and topological points of view. Indeed, the $\cap$-structure is considered as a model for all algebraic substructures such as subgroups, subrings and submodules, ideals, etc. Moreover, the elements of these $\cap$-structures are seen as an open set, and from this point of view, another goal is to relate some algebraic properties to some topological properties. The present article follows the same points of view of \cite{cap}. In particular, similar to algebraic homomorphisms, $\cap$-structural homomorphisms are defined and investigated in $\cap$-structure spaces. In addition, we examine some classical results related to homomorphisms. In this regard, similar to lattice theory, we define the congruence relation on $\cap$-structure spaces and give some facts about them, and then we generalize the isomorphism theorems of algebraic structure to $\cap$-structure spaces. https://cgasa.sbu.ac.ir/article_105052_56bfca89f626ea0096516099aef6d798.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585324120260101Pure filters and topological spaces on triangle algebras639010526910.48308/cgasa.2024.235170.1477ENFranclinDemlabi Pamba AnaniDepartment of Mathematics and Computer Science, Faculty of Science, University
of Dschang, CameroonAriane GabrielTallee KakeuDepartment of Mathematics and Computer Science, Faculty of Science, University of Dschang, Cameroon.0000-0003-4420-1835Blaise BleriotKoguep NjionouDepartment of Mathematics and Computer Science, Faculty of Science, University
of Dschang, Cameroon0000-0001-9035-6753CelestinLeleDepartment of Mathematics and Computer Science, Faculty of Science, University
of Dschang, CameroonJournal Article20240319In this paper, we delve into the lattice of filters of a triangle algebra. Moreover, we establish the prime filter theorem, and investigate the algebraic structure of the set of co-annihilators of a triangle algebra. In addition, we explore the concept of pure filter within the framework of triangle algebras. Furthermore, we describe the topological properties of the prime filter space of a triangle algebra by equipping the lattice of prime filters with the Zariski topology. Thanks to the notion of pure filters in triangle algebras, we also provide a characterization of the open stable sets with respect to the stable topology, a topology that is coarser than the Zariski topology.https://cgasa.sbu.ac.ir/article_105269_ca61678a1bd88f048400c5a8971341be.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585324120260101Category of $\mathcal{M}$-relations as a quotient of the span category9110310513410.48308/cgasa.2024.237620.1526ENNaserHosseiniDepartment of Pure Mathematics, Faculty of Math and Computers, Shahid Bahonar University of Kerman, Kerman, Iran0000-0001-8420-2061Journal Article20241119We introduce $\mathcal{M}$-spans for a class $\mathcal{M}$ of morphisms in a category $\mathcal{C}$. Using the equivalence class of $\mathcal{M}$-spans under a given equivalence relation, we give the notion of an $\mathcal{M}$-relation in $\mathcal{C}$. We first show under what conditions, $\mathcal{C}$-objects together with $\mathcal{M}$-relations form a category, called the category of $\mathcal{M}$-relations and we construct a quotient of the span category as a byproduct. Then we investigate the connection between $\mathcal{M}$-relation categories and quotient span categories. We establish when a category of $\mathcal{M}$-relations is isomorphic to a quotient span category. Finally several illustrative examples are given.https://cgasa.sbu.ac.ir/article_105134_972ac73a3daf5f4adf01d720e40db91e.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585324120260101$Z$-ideals and $Z$-congruences on semiring $\mathcal{R}^+(L)$10513510520810.48308/cgasa.2024.235948.1496ENAli AkbarEstajiFaculty of Mathematics and Computer Sciences,
Hakim Sabzevari University,
Sabzevar,
Iran.ToktamHaghdadiDepartment of Basic Sciences, Birjand University of Technology, Birjand, IranJournal Article20240606 For a frame $L$, $\mathcal{R}^+(L)$ denotes the nonnegative real valued continuous functions on $L$. We define the concept of $z$-ideals in this semiring and give a characterization of its $z$-ideals in terms of cozero elements of $L$. Also, we show that there is a one-one correspondence between $z$-ideals and $z$-congruences on a ring $\mathcal{R}(L)$ and a semiring $\mathcal{R}^+(L)$. We establish a relationship between $z$-congruence relation on $\mathcal{R}(L)$ and $z$-congruence relation on $\mathcal{R}^+(L)$. A new characterization of $P$-frames is given via $z$-congruences on $\mathcal{R}^+(L)$. Also, we show that there is a bijection between the minimal prime ideals of $\mathcal{R}(L)$ and coz-ultrafilter on $L$.https://cgasa.sbu.ac.ir/article_105208_07d63ba4b937b9f87f169cea349f575d.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585324120260101Replacing bar-like resolutions in a simplicial setting13715010545210.48308/cgasa.2024.235509.1488ENSamuelCarolusDepartment of Defense, United States of America.JacobLaubacherDepartment of Mathematics, St. Norbert College, De Pere, Wisconsin, United States of America.0000-0003-0045-7951Sydney DVitalboDepartment of Mathematics, St. Norbert College, De Pere, Wisconsin, United States of America.Leah KWidlarzDepartment of Mathematics, St. Norbert College, De Pere, Wisconsin, United States of America.Journal Article20240429It is well known that the bar resolution can be replaced with any projective resolution of the corresponding algebra when computing the Hochschild (co)homology of that algebra. This is, in fact, a feature of its construction via derived functors. For generalizations and extensions of the Hochschild (co)homology (like the secondary and tertiary Hochschild (co)homology theory, as well as higher order Hochschild (co)homology theory), one uses a bar-like resolution in a simplicial setting within its construction in order to accommodate the changing module structures in every dimension. In this note, we present a method in order to replace these bar-like resolutions.https://cgasa.sbu.ac.ir/article_105452_c36d97390a7f025c98d5b1a13740d009.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585324120260101Weakly right po-Noetherian ordered semigroups15117010532210.48308/cgasa.2024.233929.1444ENLeilaShahbazDept. of Mathematics, Faculty of Basic sciences, University of Maragheh, Maragheh, IRAN0000-0001-6312-6231Journal Article20231127In this paper, we present a new way of defining the property of being WRP-Noetherian by making use of principal right poideals. Additionally, we provide a characterization of WRP-Noetherian ordered semigroups through their $S$-posets. Furthermore, we investigate how the property of being WRP-Noetherian behaves under some semigroup-theoretic constructions, like sub ordered semigroups, and quotients. Specifically, we establish necessary and sufficient conditions for the direct product of two ordered semigroups to be WRP-Noetherian.https://cgasa.sbu.ac.ir/article_105322_a53aa0b1bf7c7e2b5e18db176edd6ea3.pdf